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

Answer:

1) The equation that represents the total area of Riley's proposed ratio is $A' = (\sqrt{2}\cdot x)\cdot (\sqrt{2}\cdot y)$.

2) The length and width of the new patio are approximately 18.4 feet and 21.2 feet, respectively.

Step-by-step explanation:

1) From Geometry we remember that area formula for the rectangle is represented by:

$A = x\cdot y$ (1)

Where:

$A$ - Area, measured in square feet.

$x$ - Length, measured in feet.

$y$ - Width, measured in feet.

From statement we know that Riley wants to double the area, that is:

$A' = 2\cdot A$ (2)

By applying (1) in (2), we get the following expression:

$A' = 2\cdot x\cdot y$ (3)

Given that Riley wants to double the area of the pation by increasing the length and width by the same amount, we can rearrange (3) by algebraic means:

$A' = \sqrt{2}\cdot \sqrt{2}\cdot x\cdot y$

$A' = (\sqrt{2}\cdot x)\cdot (\sqrt{2}\cdot y)$ (3b)

The equation that represents the total area of Riley's proposed ratio is $A' = (\sqrt{2}\cdot x)\cdot (\sqrt{2}\cdot y)$.

2) If we know that $x = 13\,ft$ and $y = 15\,ft$, then the length and the width of the new patio are, respectively:

$x' = \sqrt{2}\cdot x$

$x' = \sqrt{2}\cdot (13\,ft)$

$x' \approx 18.4\,ft$

$y' = \sqrt{2}\cdot y$

$y' = \sqrt{2}\cdot (15\,ft)$

$y' \approx 21.2\,ft$

The length and width of the new patio are approximately 18.4 feet and 21.2 feet, respectively.