Question

find the missing value x.
p 12 in. g 12 in. l
31° 31°
48 in. t
x r
x = 48
x = 24
x = 12
x = 2

Explanation:

Step1: Identify similar triangles

Since $\angle P = \angle G=31^{\circ}$ and $\angle PTL=\angle GRL$ (corresponding angles as $GR\parallel PT$), $\triangle PTL\sim\triangle GRL$.

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. We have $\frac{PG}{PL}=\frac{GR}{PT}$. Given $PG = GL = 12$ in, so $PL=PG + GL=24$ in. Let $GR = x$ and $PT = 48$ in. The proportion is $\frac{12}{24}=\frac{x}{48}$.

Step3: Solve for x

Cross - multiply: $24x=12\times48$. Then $x=\frac{12\times48}{24}$. Simplify: $x = 24$ in.

Answer:

$x = 24$