Question

PROBLEM: Riley has a rectangular shaped patio that is 13 feet long by 15 feet wide. He wants to DOUBLE THE AREA of the patio by increasing the length and width by the same amount.

1. Write an EQUATION that represents the total area of Riley's proposed patio.

2. To the NEAREST TENTH of a foot, what is the LENGTH and WIDTH of the new patio?

Answer 1

(13 + x) * (15 + x) = 390ft²

18.8 feets ; 20.8 feets

Explanation:

Given that:

Initial dimension of patio :

Length (L) = 13 feets

Width ( W) = 15 feets

Initial Area of rectangle :

Length * width = 13 * 15 = 195 feets²

To double the initial area of rectangle :

2 * 195 ft² = 390 ft²

Hence, area of proposed patio = 390ft²

Area of proposed patio:

(13 + x) * (15 + x) = 390ft²

195 + 13x + 15x + x² = 390

x² + 18x - 195 = 0

Using the quadratic equation solver:

X = - 33.77 = - 33.8 or

X = 5.77 = 5.8

X cannot be negative,

Hence, x = 5.8

Length and width of new patio:

Length = 13 + x = 13 + 5.8 = 18.8 feets

Width = 15 + x = 15 + 5.8 = 20.8 feets