Question

Which of these triangles are possible to construct by knowing only its altitude?
A) Right angled triangle
B) Equilateral triangle
C) Isosceles triangle
D) Any triangle

Answer 1

Hint:
We will check the options one by one by knowing the characteristics of each triangle. This would require the knowledge of how we construct the triangles? Which parameters or dimensions are required for it etc.so let’s check!

Complete step by step solution:
A) Right angled triangle:
This triangle is having one angle fixed of ${90}^{\circ}$. But no idea of the other two angles. Also no idea of the lengths of the other two sides. So we can’t construct.

B) Equilateral triangle:
In this triangle all sides are of the same length. Also the length of height or altitude is also the same as the side of the triangle because it divides the side into exactly two equal parts. Thus we can construct this triangle only from its altitude or height given.

C) Isosceles triangle:
In this triangle there is no relation in length of height of the triangle and the length of side. So we can’t construct.

Hence, option B is the correct answer.

Note:
Here a student needs to know the parameters of construction of a triangle. Because the steps of construction help us to know which dimensions are needed and which are not. In the case of a right angled triangle the other two angles can be of ${60}^{\circ} \text{and} {30}^{\circ}$ or of ${45}^{\circ} \text{and} {45}^{\circ}$. But we have no idea of the lengths of sides. So only the equilateral triangle can be constructed from only altitude.