Question

triangle rst has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. what is the area of triangle rst? round to the nearest square inch. herons formula: area = \sqrt{s(s - a)(s - b)(s - c)} 19 square inches 37 square inches 60 square inches 95 square inches

Explanation:

Step1: Find the third - side length

Let the sides be \(a = 22\) inches, \(b = 13\) inches, and the perimeter \(P=a + b + c=50\) inches. Then \(c=P-(a + b)=50-(22 + 13)=15\) inches.

Step2: Calculate the semi - perimeter \(s\)

The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{50}{2}=25\) inches.

Step3: Apply Heron's formula

Area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{25(25 - 22)(25 - 13)(25 - 15)}\)
\(=\sqrt{25\times3\times12\times10}=\sqrt{9000}=30\sqrt{10}\approx95\) square inches.

Answer:

D. 95 square inches