Question

Each of equal sides of an isosceles triangle is $4cm$ greater than its height. If the base of the triangle is $24cm$; calculate the perimeter (in $cm.$)

Answer 1

Let the congruent side of the isosceles triangle be a and the height be h.
Given $a=h+4$
Since the height of the triangle, divides it into two right angled triangles,
$a^2=h^2+{\left(\frac{b}{2}\right)}^2=>{(h+4)}^2=h^2+{12}^2$
$h^2+16+8h=h^2+144$
$8h=128$
$h=16cm$
$a=20cm$

Perimeter of the triangle $=$ Sum of all sides $=a+a+b$ $=20+20+24=64cm$