Question

What is the height of the triangle? 12 units 24 units 36 units 72 units.

Answer 1

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

Given information-

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is $16 \sqrt{3}$ units.

As all the sides are equal thus the $\Delta MNO$ is a equilateral triangle in which the height of the divides the triangle into two equal part of the length $8\sqrt{3}$ at point R.

Height of the triangle-

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  $\Delta MRN$, the length of the hypotenuse is $16 \sqrt{3}$ units and the length of the base is $8\sqrt{3}$ units. Let h is the height of the triangle thus by the Pythagoras theorem,

$(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2$

Solve for h,

$\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end$

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

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