Civil Engineering (CE) Exam  >  Civil Engineering (CE) Questions  >  A square has sides 5cm smaller than the sides... Start Learning for Free
A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.
  • a)
    15.10
  • b)
    18.50
  • c)
    10.00
  • d)
    8.50
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A square has sides 5cm smaller than the sides of a second square. The ...

Given,
(Area)B = 4 × (Area)A
⇒ x2 = 4(x – 5)2
⇒ x2 = 4[x2 + 25 – 10x]
⇒ x2 = 4x2 + 100 – 40x
⇒ 3x2 – 40x + 100 = 0
⇒ 3x2 – 30x – 10x + 100 = 0
⇒ 3x(x – 10) – 10(x – 10) = 0
⇒ x = 10
View all questions of this test
Most Upvoted Answer
A square has sides 5cm smaller than the sides of a second square. The ...
To solve this problem, let's assume that the side length of the smaller square is x cm.

1. Finding the area of the smaller square:
The area of a square is given by the formula A = side^2. Therefore, the area of the smaller square is x^2.

2. Finding the side length of the larger square:
According to the problem, the side length of the larger square is 5 cm longer than the side length of the smaller square. So, the side length of the larger square is (x + 5) cm.

3. Finding the area of the larger square:
The area of the larger square is four times the area of the smaller square. So, we have the equation 4(x^2) = (x + 5)^2.

4. Solving the equation:
Expanding the right side of the equation, we get 4x^2 = x^2 + 10x + 25.
Rearranging the terms, we have 3x^2 - 10x - 25 = 0.

5. Solving the quadratic equation:
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 3, b = -10, and c = -25.

Calculating the discriminant (b^2 - 4ac), we get:
b^2 - 4ac = (-10)^2 - 4(3)(-25) = 100 + 300 = 400.

Since the discriminant is positive, we have two real solutions:
x = (-(-10) ± √400) / (2(3))
x = (10 ± 20) / 6

6. Determining the side length of the larger square:
Since the side length of a square cannot be negative, we discard the negative solution and consider the positive solution:
x = (10 + 20) / 6 = 30 / 6 = 5 cm.

Therefore, the side length of the larger square is 5 cm + 5 cm = 10 cm.

7. Finding the correct answer:
The question asks for the side length of the larger square in centimeters. From our calculations, we determined that the side length of the larger square is 10 cm. Therefore, the correct answer is option C) 10.00 cm.
Explore Courses for Civil Engineering (CE) exam

Top Courses for Civil Engineering (CE)

A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer?
Question Description
A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer?.
Solutions for A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE). Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A square has sides 5cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is ________cm.a)15.10b)18.50c)10.00d)8.50Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
Explore Courses for Civil Engineering (CE) exam

Top Courses for Civil Engineering (CE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev