Question

The perimeter of a right triangle is 60 feet and the area is 150 square feet. If the lengths of the sides of the triangle are each multiplied by 10, what is the perimeter of the new right triangle?

Answer 1

600 feet.

Just multiply by 10.

Answer 2

`P_(increased)=600ft`

Explanation:

We know that the perimeter of the triangle is 60 feet, that is, the sum of all three sides is 60 feet.

Now, if each triangle is multiply by 10, that means the perimeter would be increased ten time also.

Therefore, the perimeter would be 600 feet.

If you wanna use formulas, we have

`A=150ft^(2)`

`P=60ft`

Where
`A` represents the ares and
`P` represents the perimeter.

The area of a triangle is

`A=(bh)/(2)`

Where
`b` and
`h` represent the legs of the right triangle.

`P=b+h+x\\60ft=b+h+x`

Where
`x` represents the hypothenuse of the right triangle.

After increasing sides by a scale factor of 10, the perimeter would be

`P_(increased)=10b+10h+10x`

Which shows the increasing scaling factor, then we extract this common scale factor.

`P_(increased)=10(b+h+x)`

Which means that the perimeter increased is just the old perimeter multiplied by 10, as follows

`P_(increased)=10(b+h+x)\\P_(increased)=10(60ft)=600ft`