Question

The length of a rectangle is given by a number, x (metres). The width is two metres longer than the length. The area of the rectangle is 120 m^2

Answer 1

metersGiven:

a.) The length of a rectangle is given by a number, x (meters).

b.) The width is two meters longer than the length.

c.) The area of the rectangle is 120 m^2​.

Let's first recall the formula for getting the area of the triangle.

Area = L x W

Where,

L = Length

W = Width

The width is two meters longer than the length. Therefore, we can say that:

W = L + 2

Let's now determine the measure of the dimension of the rectangle:

Let,

x = length of the rectangle

We get,

`\begin{gathered} \text{ A = L x W} \\ 120\text{ = L x (L + 2)} \\ 120=L^2\text{ + 2L} \\ L^2\text{ + 2L - 120 = 0} \\ (L\text{ - 10)(L + 12) = 0} \end{gathered}`

Based on the relationships given, the Length of the rectangle has two possible measures.

L - 10 = 0

L = 10 m

L + 12 = 0

L = -12 m

Since a length must never be a negative value, the length of the rectangle must be 10 m.

For the width, we get:

W = L + 2 = 10 + 2 = 12 m

Summary:

Length = 10 m

Width = 12 m