Question

Jacks tent is shaped like an isosceles triangle. The height of the measures 7 feet in the diagonal side measures 9 feet. Find the length of the tent's base.

Answer 1

The length of the tent's base is $8 \sqrt{2} \mathrm{ft}$

Explanation:

The tent is shaped like an isosceles triangle and measures 7 feet.

Since, isosceles triangle has two equal sides, the two sides of a triangle are 7 feet.

It is also given that the diagonal measures 9 ft.

Now, we shall determine the length of the tent's base.

Let x denote the length of the tent's base.

The image of the isosceles triangle having these measurements is attached below:

Using Pythagorean Theorem, we have,

$9^{2} =7^{2} +(\frac{x}{2} )^2$

$81=49+\frac{x^{2} }{4}$

$324=196+x^{2}$

 $x^{2} =128$

Taking square root on both sides,

$x=\sqrt{128}$

$x=8\sqrt{2}$

Thus, the length of the tent's base is $8 \sqrt{2} \mathrm{ft}$