Question 46

The sides of a triangle are 80 cm, 76 cm, and 148 cm. What is the length (in cm) of its altitude corresponding to the side with a length of 76 cm?

Name: The sides of a triangle are 80 cm, 76 cm, and 148 cm. What is the length (in cm) of its altitude corresponding to the side with a length of 76 cm?
Uploaded: 2026-06-14T11:37:30.753988+05:30
Duration: 5 min 47 s
Description: The sides of a triangle are 80 cm, 76 cm, and 148 cm. What is the length (in cm) of its altitude corresponding to the side with a length of 76 cm?

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.

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