Question

The perimeter of a right triangle is 24 ft, and one of its legs measures 6 ft. Find the length of the other leg and the hypotenuse.

a) 6 ft, 12ft
b) 5 ft, 13 ft
c) 8 ft, 10 ft
d) 7 ft, 11 ft

Answer 1

Explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

`h^2= a^2+b^2.`

and the perimeter is
`P=h+a+b`.

Since P=24 and a=6 we have these equations:

`h^2=36+b^2\\24=h+6+b`

From the last equation we have
`h=18-b`. Replace h in the first equation we get that

`(18-b)^2=36+b^2`

`18^2-36b+b^2=36+b^2\\288=36b\\b=(288)/(36)=8`

and h=18-8=10