Answer :
The length of the tent's base is [tex]$8 \sqrt{2} \mathrm{ft}$[/tex]
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,
[tex]9^{2} =7^{2} +(\frac{x}{2} )^2[/tex]
[tex]81=49+\frac{x^{2} }{4}[/tex]
[tex]324=196+x^{2}[/tex]
[tex]x^{2} =128[/tex]
Taking square root on both sides,
[tex]x=\sqrt{128}[/tex]
[tex]x=8\sqrt{2}[/tex]
Thus, the length of the tent's base is [tex]$8 \sqrt{2} \mathrm{ft}$[/tex]
