ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > ABCD is a rectangle whose longer side is AB. ...

ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?

a)
6
b)
12
c)
16
d)
20
e)
24

Correct answer is option 'B'. Can you explain this answer?

Join for Free

Join for Free

Verified Answer

ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid...

Step 1: Question statement and Inferences

Since EG is joining the midpoints of the lengths of the rectangle, it is parallel to AD and BC. (i.e., EG is perpendicular to AB and CD).

Similarly, FH is parallel to AB and CD. (FH is perpendicular to AD and BC).

Both EG and FH bisect each other at the point P.

Let the length of AE and EP be x and y respectively.

Area = 24

½ * x * y= 24

xy = 48 ------equation (1)

Note that AE = EB = HP = PF = DG = GC = x

Similarly, AH = HD = EP = PG = BF = FC = y

Perimeter of EBFP = 28

2*(x + y) = 28

(x + y) = 14 ------Equation (2)

Step 2:Finding required values

Upon substituting x = 48/y from equation (2) in equation (1),

Multiplying with y on both sides of the equation, we have

y² – 14y + 48 = 0

y² – 8y – 6y + 48 = 0

(y – 8)(y – 6) = 0

y = 8 or y = 6

Step 3: Calculating the final answer

Substituting the value of y in x = 48/y, to obtain the value of x.

If y = 8, then x = 6 and if y = 6, then x = 8.

The longer dimension is 8 units while the smaller dimension is 6 units.

Therefore BF = 6

The smaller of the sides of the rectangle = BC = 2 * 6 = 12 units

Correct Answer: B

View all questions of this test

View all answers Start learning for free

Explore Courses for GMAT exam

Similar GMAT Doubts

In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?(1) EBCF is a square of side length 5 centimeters.(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halves

View answer

The area of a triangle is equal to the area of the rectangle. Find the perimeter of the rectangle. 1. The perimeter of the square is 24 inches. 2. The sum of the length and the width is 13 inches.

View answer

Two concentric circles have their centers at point O such that a line segment AB having its end points on the outer circle touches the inner circle at point C. The length of the line segment AB istimes the radius of the inner circle. If an equilateral triangle is drawn such that the area of the triangle is equal to the ratio of the radii of the outer circle andthe inner circle respectively, what is the length of the side of the triangle?

View answer

Triangle ABC is an isosceles triangle with AB = AC and AD is the perpendicular dropped from vertex A on the side BC. What is the perimeter of triangle ABC?(1) BAD = 2ACD(2) The perimeter of triangle ADB is 15 + 53

View answer

A triangle ABC is placed inside a rectangle PQRS such that the minimum distance of any vertex of the triangle from the rectangle is 2 inches. What is the area of the rectangle PQRS?(1) Triangle ABC is an equilateral triangle(2) The area of Triangle ABC is 43 square inches and the length of the side AB of the triangle is 50% of the length of side PQ of the rectangle.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2025

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

Share with a Friend

Answer this doubt

Question Description
ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer?.

Solutions for ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer?, a detailed solution for ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice ABCD is a rectangle whose longer side is AB. E, F, G and H are the mid-points of the sides AB, BC, CD and DA respectively. The line segment joining E and G intersects with the line segment joining F and H at point P. The perimeter of the rectangle EBFP is 28 units and the area of the triangle AEP is 24 square units. What is the length of each of the smaller sides, AD and BC, of the rectangle ABCD?a)6b)12c)16d)20e)24Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam