Question

The area of a rectangle is 60 square inches. The length is x – 3, and the width is x + 8. Find the value of x, and the dimensions of the rectangle.

Answer 1

x = 7

Length = 4 inches , Width = 15 inches

Explanation:

PART 1 :

Area of rectangle = Length × Width

A = L × W

L = x - 3

W = x + 8

Therefore:

A = L × W

60 = ( x - 3 ) ( x + 8 )

( x - 3 ) ( x + 8 ) - 60 = 0

x^2 + 8x - 3x - 24 - 60 = 0

x^2 + 5x - 84 = 0

x^2 + 12x - 7x - 84 = 0

x ( x + 12 ) - 7 ( x + 12 ) = 0

( x + 12 ) ( x - 7 ) = 0

THEREFORE:

x = - 12 , x = 7

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PART 2 :

L = x - 3

L = ( - 12 ) - 3

L = - 15

OR

L = ( 7 ) - 3

L = 4

THEREFORE:

Length can not be a negative number. Hence, L can not equal to - 15.

L = 4 inches

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W = x + 8

W = ( 7 ) + 8

THEREFORE:

W = 15 inches