Question

The perimeter of an isosceles triangle is $30cm$. The length of each congruent side is $3cm$ more than the length of its base. Find the lengths of all the sides.

Answer 1

Let the congruent sides of an isosceles $△$ be $x$.
Let the base of the isosceles $△$ be $y$
According to the 1st condition,
$x+x+y=30$
$2x+y=30$
According to the 2nd condition
$x=y+3$
$x-y=3$
Solving equation (1) and (2)
$2x+y=30$
$x-y=3$
-------------------
$3x=33$
$x=\frac{33}{3}$
$x=11$
By substituting $x=11$ in equation (1)
$2x+y=30$
$2\left(11\right)+y=30$
$22+y=30$
$y=30-22$
$=8$
$\therefore$ The length of the sides of a $△$ are $11cm,11cm$ and $8cm$.