Question

A tent forms an equilateral triangular prism, with both triangular faces exposed. Each side of the triangular face has a length of 196 cm, and the tent is 250 cm long. What is the height, in centimeters, of the tent?

Answer 1

Answer:

$a=169.74cm$

Step-by-step explanation:

By the description in the problem of the tent, there are 3 rectangle faces are faces, one is the floor and the other two are formin the ceiling. This means the height of the tent can be calculated from the information of the triangular faces.

Each side of the triangle is 196 cm, if we divide the equilateral triangle into two rights triangles with a base of 196/2=98cm and a hypotenuse of 196 cm, the side missing is the height of the original equilateral triangle and also the height os the tent. Using the Pitagora's theorem:

$c^2=a^2+b^2\\a^2=c^2-b^2\\a=\sqrt{c^2-b^2}$

$a=\sqrt{196^2-98^2}=\sqrt{28812}=169.74cm$