Question

A fountain is in the shape of a right triangle. The area of the fountain is

12 square meters. One leg of the triangle measures one and a half times the
length of the other leg. What are the lengths of all three sides of the fountain?

Answer 1

4,6,
`√(52) \\`

Explanation:

Area of right triangle= base x height/2=12, but if we remove the division then it's:

base x height=24

factors of 24= 6,4 8,3 24,1 and 12,2

we have the rule that "One leg of the triangle measures one and a half times the length of the other leg." and the pair that matches that is 6 and 4.

So leg a=4 and leg b=6. Using the Pythagorean theorem(a^2+b^2=c^2) we have:

4^2+6^2=c^2=16+36=52 so the answer is 4,6,
`√(52) \\`