Question

How do you calculate the base of an isosceles triangle?

Answer 1

Hint: We have to collect all the given information of the isosceles triangle. If the perimeter and one side of an isosceles triangle is given, then we can find the base by subtracting 2 times the sides from the perimeter. If the area and the height of the isosceles triangle is given, then we can find the base by dividing 2 times the area by the height.

Complete step by step solution:
According to the question, we are asked to find the base of an isosceles triangle.
We know that the isosceles triangle has two sides equal other than the base.
Consider the length of the sides to be x.
And the base of the isosceles triangle is b.
The height of the isosceles triangle is h.

To find the base of the isosceles triangle, we have to look for the given information.
There are two cases.
CASE 1
If the perimeter of the triangle is given, say P and the length is given, then we can find the base.
We know that perimeter is the sum of all the sides of the triangle.
\[P=a+a+b\]
\[\Rightarrow P=2a+b\]
Therefore, the base of the isosceles triangle is
b=P-2a
Thus, we get the base of the triangle.
CASE 2
If the area of the isosceles triangle is given with height h of the triangle, we can find the base.
We know that area of a triangle is
\[A=\dfrac{1}{2}\times bh\]
To find the base, we have to multiply 2 on both the sides.
\[\Rightarrow 2A=\dfrac{2}{2}\times bh\]
On cancelling 2 from the numerator and denominator, we get
\[2A=bh\]
Now, divide h on both the sides of the expression.
\[\dfrac{2A}{h}=\dfrac{bh}{h}\]
Cancel h from the numerator and denominator of the RHS.
\[\Rightarrow \dfrac{2A}{h}=b\]
\[b=\dfrac{2A}{h}\]
Therefore, the base of an isosceles triangle when area and height is given is \[\dfrac{2A}{h}\]. Hence, we can find the base of an isosceles triangle if sufficient information is given.

Note: We can also find the length of the base if the area and the angle between the base and the sides are given. We have to use the formula according to the information given. Do the calculations carefully to get the accurate answer.