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

1 Answer
Sep 20, 2017

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!