Question

if the area of an isosceles triangle is 60 centimetres square and the length of each of its equal sides is 13 cm find its base

Answer 1

area of the isosceles triangle (A) = 60 cm²
length of the each equal side = a = 13cm
let  length of the base = b cm

b/4( √4a² - b² ) = A

b/4 (√4*(13)² - b² ) = 60 cm²
do the square both sides
b²/16 (4*169 -b²) = 3600
b²(676 - b²) =16 *3600
let b² = x

x(676 -x ) =57600 
676x -x² =57600
rearreanging the terms
x²-676x +57600 =0
x² -576x -100x+57600=0
x(x-576)-100(x-576) =0
(x-576) (x-100) =0
x-576 =0 or x- 100 =0
x= 576 or x= 100

b²=576 or b² =100
b²= 24² or b² =10²

b= 24cm or b=10 cm