Question

A wooden stage rests on a triangular stilt. The base of the triangle is the same as the height. The area of the stilt is 24.5 square meters. What is the height of the triangle?

Answer 1

The height of the triangle is 7m.

Answer 2

The height of the triangle is 7 m.

Explanation:

Given a triangle with dimension of the base (b) equal to that of height (h) and an area of 24.5 m². You have to evaluate this information in terms of the equation that describes the area of a triangle (A).

A = (b×h)/2 ⇒ replacing with the value of area given before

24.5 m² = (bxh)/2 ⇒ (24.5 m²) x 2 = bxh ⇒ 49 m² = bxh.

As the base has the same dimension as height, we can write bxh= b² or h²

⇒49 m² = b²⇒ √(49 m²) = b ⇒ 7 m = b = h.

Summarizing the height of the triangle is 7 m.