Question 46
The sides of a triangle are 80 cm, 76 cm, and 148 cm. What is the length (incm) of its altitude corresponding to the side with a length of 76 cm?264
Solution
Area of a triangle = half of Base x Height.
Area is also equal to $$\sqrt{\ s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$$.
Semi perimeter for the triangle = half of (80+76+148) = 152.
So, $$\frac{1}{2}\times\ 76\times\ H=\sqrt{\ 152\times\ 72\times\ 76\times\ 4}$$
This gives H = 48 cm.
