# Two isosceles triangles have the same base length. The legs of one of the triangles are twice as long as the legs of the other. How do you find the lengths of the sides of the triangles if their perimeters are 23 cm and 41 cm?

Oct 24, 2016

the sides of smaller isocelles triangle are $\left(5 , 9 , 9\right) c m$
and of bigger isocelles triangle are $\left(5 , 18 , 18\right) c m$

#### Explanation:

Let the sides of smaller isocelles triangle are $a , b , b$
The perimeter of smaller isocelles triangle is $a + b + b = 23 \mathmr{and} a + 2 b = 23 \left(1\right)$

Then, the sides of bigger isocelles triangle are $a , 2 b , 2 b$
The perimeter of bigger isocelles triangle is $a + 2 b + 2 b = 41 \mathmr{and} a + 4 b = 41 \left(2\right)$
Subtracting (1) from (2) we get $2 b = 18 \mathmr{and} b = 9 \therefore a = 23 - 2 \cdot 9 = 5$

Hence the sides of smaller isocelles triangle are $\left(5 , 9 , 9\right) c m$
and the sides of bigger isocelles triangle are $\left(5 , 18 , 18\right) c m$ [Ans]