Question

b. trapezoid
2 - 108. solve for the missing lengths. show all work. homework help
a. $delta ghisimdelta pqr$
b. $delta abcsimdelta xyz$

Explanation:

Step1: Recall similarity - ratio property

For similar triangles $\triangle GHI\sim\triangle PQR$, the ratios of corresponding sides are equal. Let the sides of $\triangle GHI$ be $GH = 7$, $GI=2$, $HI = 1$ and the sides of $\triangle PQR$ be $PQ = 112$, $PR=n$, $QR$. Then $\frac{GH}{PQ}=\frac{GI}{PR}=\frac{HI}{QR}$.
We use $\frac{GH}{PQ}=\frac{GI}{PR}$, so $\frac{7}{112}=\frac{2}{n}$.

Step2: Cross - multiply to solve for $n$

Cross - multiplying gives $7n=2\times112$.
$7n = 224$.
Dividing both sides by 7, we get $n=\frac{224}{7}=32$.

For similar triangles $\triangle ABC\sim\triangle XYZ$, let $AB = 7$, $AC = 23$, $BC$ and $XY=m$, $XZ = 49$, $YZ$. Using the ratio of corresponding sides $\frac{AB}{XY}=\frac{AC}{XZ}$.
So $\frac{7}{m}=\frac{23}{49}$.

Step3: Cross - multiply to solve for $m$

Cross - multiplying gives $23m=7\times49$.
$23m = 343$.
Then $m=\frac{343}{23}\approx14.91$.

Answer:

$n = 32$, $m=\frac{343}{23}\approx14.91$