A builder wants to increase the size of one of his square patios. The patio measures 16 feet on each side. The builder plans to increase each side of the patio to be 125% of its current measure.
How many square feet larger is the area of the new patio than the area of the current patio?
a) 64 ft²
b) 144 ft²
c) 320ft²
d) 656 ft²

Question

Shadow · Answer

Do  16 times 1.25 or do 16 times 5/4

This will give you 125% of 16. Then just calculate for the new area with the new side

$$A_{s} = s^2$$
Area of a square = side squared

Shadow · Answer

Next you'll have to solve for the original size of the patio if you haven't already, so, just do 16^2.

Then just do: new patio size - old patio size = difference between the patios

chuckthedonut · Answer

Okay, so I did 16 times 1.25, and I got 20. What now?

Shadow · Answer

Since all sides of a square are equal, you now have both the length and the width of the square. You can then calculate for the area of the new patio. So just do A = 20^2

chuckthedonut · Answer

@shadow wrote:

Since all sides of a square are equal, you now have both the length and the width of the square. You can then calculate for the area of the new patio. So just do A = 20^2

well 20^2 = 400

Shadow · Answer

Correct. Now since they're asking for: How many square feet larger is the area of the new patio than the area of the current patio?

We need the area of the current patio, and not the new patio.

Shadow · Answer

Then we can do: new patio size - old patio size = difference between the patios

chuckthedonut · Answer

@shadow wrote:

Then we can do: new patio size - old patio size = difference between the patios

Ohh okay- so what equation/math will i do for that?

Shadow · Answer

Did you solve for the area of the current patio

chuckthedonut · Answer

@shadow wrote:

Did you solve for the area of the current patio

How do i do that? Do I take 20 and 400 and multiply?

Shadow · Answer

Remember the current patio has the side lengths of 16. The new patio has side lengths 125% larger, which is why you did 16 times 1.25, which got you 20.

chuckthedonut · Answer

@shadow wrote:

Remember the current patio has the side lengths of 16. The new patio has side lengths 125% larger, which is why you did 16 times 1.25, which got you 20.

I'm confused...so i do the same thing? (sorry lol)

Shadow · Answer

Yeah, they want to find out how much larger the new patio is than the current one. So yeah, you need the area of the current one.

chuckthedonut · Answer

@shadow wrote:

Yeah, they want to find out how much larger the new patio is than the current one. So yeah, you need the area of the current one.

What numbers am i using for the current one?

Shadow · Answer

"A builder wants to increase the size of one of his square patios. The patio measures 16 feet on each side."

chuckthedonut · Answer

@shadow wrote:

"A builder wants to increase the size of one of his square patios. The patio measures 16 feet on each side."

So im using 16 x another number

Shadow · Answer

Yes

chuckthedonut · Answer

@shadow wrote:

Yes

16x20?

Shadow · Answer

No.

That is a rectangle.

|dw:1678481653956:dw|

We're talking about a square, whose all sides are 16

chuckthedonut · Answer

@shadow wrote:

No. That is a rectangle. Created with RaphaëlReply Using Drawing We're talking about a square, whose all sides are 16

16x16=256

Shadow · Answer

Yes. Then take the area of the new patio (400) and subtract the area of the current patio from it (256)

So 400 - 256

chuckthedonut · Answer

@shadow wrote:

Yes. Then take the area of the new patio (400) and subtract the area of the current patio from it (256) So 400 - 256

144

chuckthedonut · Answer

@chuckthedonut wrote:

@shadow wrote:

Yes. Then take the area of the new patio (400) and subtract the area of the current patio from it (256) So 400 - 256

144

so the answer is 144

Shadow · Answer

Yes

chuckthedonut · Answer

@shadow wrote:

Yes

Okay, tysm for your detailed explanations! I will write this all down so i can remember

Shadow · Answer

You're welcome