PQR is an isosceles triangle such that QP=QR=13 CM and the altitude is PS=12cm.. find the length of PR

Question

Its about triangles. Pythagoras theorem and the lengths and distances

Answer 1

draw isosceles triangle PQR (note: PQ=PR=13 cm)

draw altitude PS which bisects segment QR

find the length of QR

so, QS=SR

triangle PSR is a right triangle

13^2=12^2+SR^2

169=144+SR^2

169-144=SR^2

25=SR^2

SR=√25

SR=5 and QR=10 cm

Answer 2

Hmmm.  If you mean that the height of the triangle is 12, then P's theorem says:

 

12^2 + x^2 = 13^2

144 + x^2 = 169

x^2 = 25

x = 5

PR = 10