What are the dimensions of both the rectangle and the square? (Read the rest in description)

Question

A rectangle is three times as long as it is wide and has the same perimeter as a square whose area is 25 square feet

larger than that of the rectangle. What are the dimensions of both the rectangle and the square?

Answer 1

Let    x = width of the rectangle

then 3x = length of the rectangle

thus 8x = perimeter of the rectangle = perimeter of the square

thus 2x = side of the square

 

       (3x)(x) = 3x² = area of the rectangle

 

       (2x)(2x) = 4x² = area of the square

 

area of the square is 25 square feet larger than the area of the rectangle

 

             4x²  = 3x² + 25

                x² = 25

                 x = 5

 

Thus dimensions of the rectangle as 15' by 5', the dimensions of the square is 10' by 10'. 

Answer 2

square area = s²

square dimension = 4 * s

rectangle area = l * w

rectangle dimension = 2 * (l + w)

 

Given:

l = 3 * w

2 * (l + w) = 4 * s

(l * w) + 25 = s²

 

Substitute the first equation with the second equation

2(3w + w) = 4s

8w = 4s

2w = s

 

Substitute "2w = s" into the 3rd equation

(3w * w) + 25 = (2w)²

3w² + 25 = 4w²

25 = w²

5 = w

 

Find l

l = 3 * 5

l = 15

 

Find s

2 * (15 + 5) = 4 * s

40 = 4s

s = 10

 

w = 5, l = 15, s = 10

Square dimension: 4 * s = 4 * 10 = 40 feet

Rectangle dimension = 2 (l + w) = 2 (15 + 5) = 40 feet