Question

You Try! As an Equation Example B: A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet. Find the dimensions of the rectangle. Write an equation to model this problem and solve it in the sketch area below. 市里。 Entrega

Answer 1

Let the width be w and the length be l

Since the width is 5ft less than the length,

then

w=l-5

The area of the rectangle is 126 square feet

Then

l times w = 126

therefore

l(l-5) = 126

`\begin{gathered} \Rightarrow l^2-5l=126 \\ \Rightarrow l^2-5l-126=0 \end{gathered}`

Factorising the equation, we have:

`\begin{gathered} l^2+9l-14l-126=0 \\ \Rightarrow(l+9)(l-14)=0 \\ \Rightarrow l=-9\text{ or 14} \end{gathered}`

Since l cannot be negative

then the only correct option is l=14

Since w = l - 5

then

w = 14 - 5 = 9

Therefore the length is 14ft and the width is 9ft