The length of the tent's base is ![$8 \sqrt{2} \mathrm{ft}$](https://tex.z-dn.net/?f=%248%20%5Csqrt%7B2%7D%20%5Cmathrm%7Bft%7D%24)
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](https://tex.z-dn.net/?f=9%5E%7B2%7D%20%3D7%5E%7B2%7D%20%2B%28%5Cfrac%7Bx%7D%7B2%7D%20%29%5E2)
![81=49+\frac{x^{2} }{4}](https://tex.z-dn.net/?f=81%3D49%2B%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B4%7D)
![324=196+x^{2}](https://tex.z-dn.net/?f=324%3D196%2Bx%5E%7B2%7D)
![x^{2} =128](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D128)
Taking square root on both sides,
![x=\sqrt{128}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B128%7D)
![x=8\sqrt{2}](https://tex.z-dn.net/?f=x%3D8%5Csqrt%7B2%7D)
Thus, the length of the tent's base is ![$8 \sqrt{2} \mathrm{ft}$](https://tex.z-dn.net/?f=%248%20%5Csqrt%7B2%7D%20%5Cmathrm%7Bft%7D%24)