Question

Yael has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length, to the nearest tenth, of one side of the new garage?

Answer 1

Answer: Length of new square = 19 feet.

Step-by-step explanation:

Since we have given that

Area of floor space = 228 square feet

If we increase the floor space by 50%

then our new area of floor space is given by

$228\times \frac{100+50}{100}\\\\=228\times \frac{150}{100}\\\\=\frac{34200}{100}\\\\=342$

So, side of new square will be

$\text{ Area of square }\\\\342=Side\times Side\\\\342=Side^2\\\\\sqrt{342}=Side\\\\18.5=Side\\\\19=Side(\text{ nearest tenth})$

Answer 2

Answer:

18.5 feet.

Step-by-step explanation:

Let x represent side length of new garage.

We have been given Yael has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%.

The area of new garage after 50% increase would be 228 plus 50% of 228.

We know that area of square is product of its side length. We can represent this information in an equation as:

$x\cdot x=228+\frac{50}{100}\cdot 228$

$x^2=228+0.50\cdot 228$

$x^2=228+114$

$x^2=342$

Take square root of both sides:

$x=\sqrt{342}$

$x=18.493242$

$x\approx 18.5$

Therefore, the length of each side of new garage would be 18.5 feet.