"Oscars Dog House Is Shaped Like A Tent. The Slanted Sides Are Both 5 Feet Long And The Bottom Of The House Is 6 Feet Across. What Is The Height Of Hi

July 21, 2022

Oscars dog house is shaped like a tent. The slanted sides are both 5 feet long and the bottom of the house is 6 feet across. What is the height of his dog house, in feet, at its tallest point?

Answer:

The answer to this problem is 2.65 ft.

Step-by-step explanation:

This problem is best illustrated with the photo below. Assuming that the tent is a square pyramid, the solution for this problem goes like this

Let d = diagonal of the square base

and h = height of the tent

First, let us solve for the diagonal of the base. Since the diagonal of a square is just the side multiplied by $\sqrt{2}$ , then d = $6\sqrt{2}$ .

Next, we can observe that the half of the diagonal and the height forms a right triangle having the slanted side as the hypotenuse. Thus, we can use the Pythagorean theorem to solve for h.

$h^2 = 5^2 - (\frac{6\sqrt{2} }{2})^2\\h^2 = 7\\h = \sqrt{7}\\h = 2.65 ft$