Question

The are of a shaded region is 118 ft squared. Which equation can be- used to find the value of X, in feet?

Answer 1

`x^2+ 18x -130=0`

Explanation:

Given

See attachment for diagram

Required

The equation to find x

First, calculate the area of the big rectangle using:

`Area = Length * Width`

So:

`A_1 = (x + 6) * (3x - 2)`

The smaller rectangle

`A_2 = (x - 1) * (2x)`

The difference between this areas give the area of the shaded region.

So:

`A_1 - A_1 = 118`

`(x+6)*(3x-2) - (x-1)*2x = 118`

Open brackets

`3x^2 - 2x + 18x -12 -2x^2 +2x = 118`

Collect like terms

`3x^2 -2x^2- 2x +2x+ 18x -12 - 118=0`

`x^2+ 18x -130=0`

The above equation can be used to solve for x