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

18.8 ft

20.8 ft

Step-by-step explanation:

Given that :

Dimension of rectangular patio:

13 feets * 15 feets

To double the area of The patio :

2 * initial. Area

Initial Area = area of rectangle = Length * width

Initial area = 13 * 15 = 195ft²

New area of patio = 2 * 195 ft² = 390 ft²

To obtain the new area, the length and width of patio increased in equal amount:

Let the Increment = x

Hence,

(length + x) * (width + x) = 390

(13 + x) * (15 + x) = 390

195 + 13x + 15x + x² = 390

195 + 13x + 15x + x² - 390 = 0

x² + 28x - 195 = 0

Using the quadratic equation solver to save computation time :

The roots are :

X = - 33.773 or 5.773

Dimension can't be negative, hence,

x = 5.773

New dimension :

(length + x) = 13 + 5.773 = 18.8 ft

(width + x) = 15 + 5.773 = 20.8 ft

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)