Question

The length of a rectangle is 7cm longer than it’s width and the area of the rectangle is 240 m ^2 fond the exact dimensions of the regtangleWidth ?cm Length? Cm

Answer 1

Let:

L = Length

W = Width

The length is 7cm longer than its width, so:

$L=W+7$

The area is given by:

$A=W\cdot L$

Therefore:

$\begin{gathered} 240=(W+7)\cdot(W) \\ 240=W^2+7W \\ W^2+7W-240=0 \end{gathered}$

Solve for W using the quadratic formula:

$\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ W=\frac{-7\pm\sqrt[]{7^2-4(1)(-240)}}{2(1)} \\ W=\frac{-7\pm\sqrt[]{1009}}{2} \\ W\approx12.38238 \\ or \\ W\approx-19.38238 \end{gathered}$

Therefore:

W = 12.38238 since a negative width wouldn't make any sense

and:

$\begin{gathered} L=W+7 \\ L=19.38238 \end{gathered}$

Answer:

W = 12.38238 m

L = 19.38238 m