Question

The area of an isosceles triangle is 60 square meters. One of the equal sides is is 13 cm. Find the third side. Take base x then h = √13² - x²

Answer 1

Let 2x be the length of third side

\(h=\sqrt{13^2-x^2}\)

Area of the right angled triangle = 30

Substitute x² = a

a² - 169a + 3600 = 0

\(a=\frac{169\pm \sqrt{28651-14400}}{2}\) = \(\frac{169\pm119}{2}=144,25\) 

If a = 144, then x = 12

If a = 25, then x = 5

Third side of the triangle = 24 cm or 10 cm.