Question

find the perimeter of $\triangle fgh$. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.
(there are two triangles in the image: $\triangle ecd$ with angles $71^\circ$ at e, $60^\circ$ at c, $49^\circ$ at d, and sides 97, 120, 111; $\triangle fgh$ with angles $71^\circ$ at h, $49^\circ$ at g, $60^\circ$ at f, and sides 99.9, 108, and x (fh).)

Explanation:

Step1: Verify triangle similarity

First, confirm $\triangle EDC \sim \triangle HGF$:

• $\angle E = \angle H = 71^\circ$, $\angle D = \angle G = 49^\circ$, $\angle C = \angle F = 60^\circ$ (all corresponding angles are equal, so AA similarity applies).

Step2: Find similarity ratio

Calculate the ratio of corresponding sides:
$\text{Ratio} = \frac{GH}{ED} = \frac{99.9}{111} = 0.9$

Step3: Solve for side $x$

Use the ratio to find $x$ (corresponds to $DC$):
$x = 120 \times 0.9 = 108$

Step4: Calculate perimeter of $\triangle FGH$

Sum all sides of $\triangle FGH$:
$\text{Perimeter} = 99.9 + 108 + 108$

Answer:

315.9