A rectangle is 3 times as long as it is wide and has the sam

A rectangle is 3 times as long as it is wide and has the same perimeter as a square whose area is 64 square feet larger than the area of the rectangle. What are the dimensions of the rectangle; Length and Width?

Solution

Let rectangle width = x ft

Length = 3x ft

Area = length x width

= 3x . x

= 3x² square ft

Let side of square = a ft

Perimeter of rectangle = Perimeter of square

2( x + 3x ) = 4a

8x = 4a

x = 4a/8

x = a/2

Area of square = Area of rectangle + 64 square ft

= 3x² + 64

= 3(a/2)² + 64

= ( 3a²/4 ) + 64

= ( 48a² + 64 ) / 64

We know that

Area of square = a²

Hence ,

a² =  ( 48a² + 64 ) / 64

64a² =  48a² + 64

64a² - 48a² = 64

16a² = 64

a² = 64/16

a² = 4

a = 2

Hence ,

x = a/2

= 2/2

= 1

Width x = 1 ft

Length 3x = 3.1 = 3ft

Therefore ,

Length = 3 ft

Width = 1 ft