Posted by Denis Borris on November 13, 2002 at 00:26:35:
In Reply to: area of an isosceles triangle posted by ipshi on November 12, 2002 at 23:36:32:
: The area of an isosceles triangle is 60 sq.cm with the two equal sides having
: length of 13cm each. What is the length of the base?
Friends of Pytagoras will instantly see 2 rights of 5-12-13 stuck together;
however:
b = base, h = height; then:
bh/2 = 60 ; h = 120/b [1]
and:
h^2 + (b/2)^2 = 13^2 ; subs [1]:
(120/b)^2 + (b/2)^2 = 169 ; simplify:
b^4 - 676b^2 + 57600 = 0 ; factor:
(b^2 - 100)(b^2 - 576) = 0
b^2 = 100 or 576
b = 10 or 24
BOTH are correct: can you see why?