Question

The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle.

Answer 1

let the length and width of the rectangle be L and w

given:

w = L-5

Area = 150 sq inches

area of the rectangle = L*w

150 = L*(L-5)

150 = L squared -5l

L squared - 150 = 0

L squared - 15L+10L -150 = 0

L(L-15)+10(L-15)= 0

(L+10)(L-15)=0

(L+10 )= 0 or (L-15) = 0

L = -10 is not possible as there wont be negative lengths

so L = 15

there fore w = L - 5 = 15 - 5 = 10

L = 15 in and w = 10 in

Answer 2

The length is 15 and the width is 10

Explanation:

Let l = length

w = l-5

We know the area is 150

A = l*w

150 = l ( l-5)

150 = l^2 - 5l

Subtract 150 from each side

0 = l^2 - 5l - 150

Factor

0= ( l+10) ( l-15)

Using the zero product property

l+10 =0 l-15=0

l = -10 l = 15

Since we cannot have a negative length

l = 15

w = 15-5 = 10

The length is 15 and the width is 10