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

18.5 feet.

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+(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=√(342)`

`x=18.493242`

`x\approx 18.5`

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

Answer 2

Answer: Length of new square = 19 feet.

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* (100+50)/(100)\\\\=228* (150)/(100)\\\\=(34200)/(100)\\\\=342`

So, side of new square will be

`\text{ Area of square }\\\\342=Side* Side\\\\342=Side^2\\\\√(342)=Side\\\\18.5=Side\\\\19=Side(\text{ nearest tenth})`