How can I determine the length of the sides $b$, and the altitude $h$ of an isosceles triangle given its area $A= 24 \text{cm}^2$ and its perimeter $P= 16\text{cm}$?
[Math] Find the length of the sides in an Isosceles triangle, given its area and perimeter
triangles
Best Answer
Let $a$ be the length of one side and let $b$ be the length of the other two sides, and let $h$ be the altitude.
By Pythagorean Theorem we have that $$\left(\frac{1}{2}a\right)^2 + h^2 = b^2$$
We also have that $a + 2b = 16$ and $\dfrac{1}{2}ah = 24$.
Solve this system of $3$ equations.