Question

The length of a rectangle is 5 inches longer than it is wide. If the area is 150 square inches, what are the dimensions of the rectangle?

Answer 1

Answer:

Step-by-step explanation:

Let width = w in

Length = w + 5 in

Area of rectangle = 150 square inches

length * width = 150

(w +5) * w  = 150

w*w + w*5 = 150

w² + 5w -150 = 0

Sum = 5

Product = -150

Factors = 15 , -10

w² + 5w - 150 = 0

w² + 15w - 10w - 10*15 = 0

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

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

Ignore w +15 because measurement won't come in negative

Therefore, w - 10 = 0

                    w = 10 inches

length = w + 5 = 10 +5 = 15 inches

Length = 15 inches

Width = 10 inches

Answer 2

Answer:

Width: 10 inches

Length: 15 inches

Step-by-step explanation:

Let the width be w.

Since the length is 5 inches longer than its width, the length = w +5.

Area of rectangle = length x width

w (w +5) = 150

w^2 + 5w = 150

w^2 + 5w -150 = 0

Using quadratic formula,

w = 10 or -15

Since the width cannot be negative,

the width is 10 inches.

Now just substitute w=10 into length = w +5.

length = 10 + 5

= 15 inches