Question

You decide to build a rectangular garden in your backyard. You've designated an area of 180m^2 for your garden. Due to the configuration of your backyard, the width of the garden must be 8 meters less than the length.

Answer 1

Answer:

$Length = 18m$

$Width = 10m$

Step-by-step explanation:

Given

$Area = 180m^2$

$Width = Length - 8$

Required

Determine the Length and the Width

Represent Width with W and Length with L;

So, we have:

$Area = L * W$

$Area = L * (L - 8)$

$180 = L * (L - 8)$

$180 = L^2 - 8L$

$L^2 - 8L - 180 = 0$

Expand

$L^2 - 18L + 10L- 180 = 0$

$L(L - 18) + 10(L- 18) = 0$

$(L + 10)(L- 18) = 0$

Split

$L + 10 =0$ or $L - 18 = 0$

$L = -10$ or $L = 18$

But length cant be negative:

So,

$L = 18$

Recall that:

$Width = Length - 8$

$W = 18 - 8$

$W = 10$

Hence:

$Length = 18m$

$Width = 10m$