Question

fall 2025 geometry b wwva area and perimeter of triangles the area of triangle efg is 34.8 square units. what is the perimeter of triangle efg to the nearest unit? 60 units 30 units 41 units

Explanation:

Step1: Recall area formula

The area formula for a triangle is $A=\frac{1}{2}ab\sin C$. Let $a = 10$, $b$ be the unknown side adjacent to the $56^{\circ}$ - angle, and $C = 56^{\circ}$. We know $A = 34.8$. So, $34.8=\frac{1}{2}\times10\times b\times\sin(56^{\circ})$.

Step2: Solve for unknown side

First, $\sin(56^{\circ})\approx0.829$. Then, $34.8 = 5\times b\times0.829$. So, $b=\frac{34.8}{5\times0.829}=\frac{34.8}{4.145}\approx8.4$.

Step3: Calculate perimeter

The perimeter $P$ of a triangle with side - lengths $a = 10$, $b\approx8.4$, and $c = 12$ is $P=a + b + c=10 + 8.4+12=30.4\approx30$.

Answer:

30 units