Question

triangle pqr has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. what is the area of triangle pqr? round to the nearest square foot. herons formula: area = $sqrt{s(s - a)(s - b)(s - c)}$ 6 square feet 7 square feet 19 square feet 22 square feet

Explanation:

Answer:

First, find the third - side length. Let the sides be \(a = 9\), \(b = 10\), and the perimeter \(P=a + b + c=24\). Then \(c=24-(9 + 10)=5\).
The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{24}{2}=12\).
Using Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\), we substitute \(s = 12\), \(a = 9\), \(b = 10\), and \(c = 5\):
\(A=\sqrt{12(12 - 9)(12 - 10)(12 - 5)}=\sqrt{12\times3\times2\times7}=\sqrt{504}\approx22\) square feet.
So the answer is 22 square feet.