Question

How do you calculate the height of an isosceles triangle?

Answer 1

Hint: Here, we are required to calculate the height of an isosceles triangle. We will use the definition of an isosceles triangle and the method of calculating the area of a triangle. We will then substitute the known area and base to find the required height of the isosceles triangle.

Formula Used:
Area of triangle, $A={\displaystyle \frac{1}{2}}\times b\times h$
Where, $b,h$ are the base and height of the triangle respectively.

Complete step by step solution:
We know that an isosceles triangle is a triangle in which we have two equal sides and two equal angles.
Now, we know that area of triangle, $A={\displaystyle \frac{1}{2}}\times b\times h$
Here, multiplying both sides by 2 and then, dividing both sides by $b$, we get,
$\Rightarrow {\displaystyle \frac{2A}{b}}=h$

Therefore, in order to calculate the height of an isosceles triangle, we can multiply the area of the triangle by 2 and divide the product by the base of the triangle to find the required height.

Note:
An alternate way of finding the height of an isosceles triangle is:
As we know, the height of an isosceles triangle splits the entire triangle into two congruent triangles. Hence, in order to find the height, we can use the Pythagoras theorem, hence, we will get:
$h=\sqrt{l^2-b^2}$
Where, $l,b,h$ are the length, base, and height of the triangle respectively
Also, we used the Pythagoras theorem because the height of a triangle is always perpendicular to the base and thus, divides the triangle into two right congruent triangles.
Thus, using this can also help us to find the height of an isosceles triangle.