Question

An isosceles triangle has exactly two sides that are equal in length​ (congruent). If the base​ (the third​ side) measures 41 inches and the perimeter is 93 ​inches, find the length of the two congruent​ sides, called legs?

word problem

Answer 1

Length = 26 inches

Explanation:

We can make this worded question into a mathematical one. If we let `P` equal the perimeter, `b` equal the non-congruent side-length, and `x` equal one congruent side-length, we get
`P=b+x+x`
`P=b+2x`

We know that `P=93` and `b=41`, so if we plug them into the equation we get
`93=41+2x`. Subtract 41 from both sides to get
`52=2x`. Divide both sides by 2 to get
`26=x`. There you have it, the length of one congruent side, or leg, is 26 inches. Obviously, this means the length of both congruent legs combined equals 52 inches.

I hope I helped!