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 = $sqrt{s(s - a)(s - b)(s - c)}$
o 6 square feet
o 7 square feet
o 19 square feet
o 22 square feet

Explanation:

Step1: Find the third - side length

Let the sides be $a = 9$, $b = 10$, and the perimeter $P=24$. The third - side $c=P-(a + b)=24-(9 + 10)=5$.

Step2: Calculate the semi - perimeter $s$

The semi - perimeter $s=\frac{a + b + c}{2}=\frac{9+10 + 5}{2}=\frac{24}{2}=12$.

Step3: Apply Heron's formula

Using Heron's formula $A=\sqrt{s(s - a)(s - b)(s - c)}$, substitute $s = 12$, $a = 9$, $b = 10$, and $c = 5$.
$A=\sqrt{12(12 - 9)(12 - 10)(12 - 5)}=\sqrt{12\times3\times2\times7}=\sqrt{504}\approx22.45$.

Answer:

D. 22 square feet