In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2andradic;2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2andradic;2b)4c)4andradic;2d)8e)16Correct 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 > In the figure given above, the diagonal AC an...

In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?

a)
2√2
b)
4
c)
4√2
d)
8
e)
16

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

Join for Free

Join for Free

Verified Answer

In the figure given above, the diagonal AC and side DC of square ABCD ...

Given

Approach

We know that area of square ABCD = side . So, if we can find the area of triangle CEF, we can find the area of square ABCD, which will give us the side length of square ABCD.
In triangle CEF, we only know the side length CF. So, we need to find the lengths of other sides and the angles of the triangle.
Now, we know that diagonals of a square bisects its angles. Also, since AE and DF are straight intersecting lines, ∠ECF = ∠DCA (vertically opposite angles)
1. Since we now know ∠ECF, we can calculate the other angles of the
  triangle CEF.

Working out

As the diagonals of the square bisect the vertex angles, ∠DCA = 45⁰
1. Since ∠ECF and ∠DCA are vertically opposite angles, ∠ECF = ∠DCA = 45⁰

3. So, triangle CEF is an isosceles right angled triangle with its hypotenuse equal to 2√2
Using the 45^o - 45^o- 90^otriangle property, we have CE= EF = 2

4. Hence, area of triangle CEF = ½ * CE * EF = ½ * 2* 2 = 2 square centimeters

5. Using the relation

we have Ar(ABCD) = 16

6. Thus, side of square ABCD = √16 = 4 centimeters

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 figure above, triangle ABC is an isosceles triangle with AB = BC and BD is the perpendicular dropped from vertex B to the side AC. Point E is marked on BD such that ∠DAE = 450and∠ECB = 150. If the ratio of length CD: BD = 1: √3.What is the ratio of the area of triangle BECto the area of the triangle ABC?

View answer

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

In the figure above, rectangle PQRS is a shaded region inside the square ABCD. What is the probability that a point chosen at random from the square ABCD will lie inside the shaded rectangle PQRS?(1) The length of a diagonal of rectangle PQRS is 55% the length of a diagonal of square ABCD(2) The length of side PQ is 20% greater than the length of side QR

View answer

What is the value of a?(1) The area of an equilateral triangle of side length 3a units is 9√3square units(2) The area of an isosceles triangle whose sides are of length 4a, 4a and a units is 3√7square units

View answer

In the figure above, triangle ABC is inscribed in a circle whose centre O has the x- and y-coordinates as (0,0). If the x- and y- coordinates of point A are (-4,0) and ∠BAC = 30, what is the area, in square units, of triangle AOB?

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
In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct 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 In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct 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 In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct answer is option 'B'. Can you explain this answer?.

Solutions for In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct 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 In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct answer is option 'B'. Can you explain this answer?, a detailed solution for In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In the figure given above, the diagonal AC and side DC of square ABCD are extended to form sides of the isosceles triangle CEF where CE = EF. If the length of side CF is 2√2 and the ratio of areas of the triangle CEF to the square ABCD is 1:8, what is the length of the side of square ABCD?a)2√2b)4c)4√2d)8e)16Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam