Question

word problems, similar triangles (level 1)
score: 3/4 penalty: 0.5 off
question
to indirectly measure the distance across a lake, lauren makes use of a couple landmarks at points h and i. she measures gj, jh, and jk as marked. find the distance across the lake (hi), rounding your answer to the nearest hundredth of a meter.
(diagram is not to scale.)
answer attempt 1 out of 2
hi = m submit answer

Explanation:

Step1: Identify similar triangles

Triangles $\triangle GJH$ and $\triangle GKI$ are similar because $\angle G$ is common and $\angle J = \angle K=90^{\circ}$.

Step2: Set up proportion

The ratio of corresponding sides of similar triangles is equal. So, $\frac{HI}{JK}=\frac{JH}{JG}$. We know $JH = 95$ m, $JG=125$ m and $JK = 109.5$ m. Let $HI=x$. Then $\frac{x}{109.5}=\frac{95}{125}$.

Step3: Solve for $HI$

Cross - multiply: $125x=95\times109.5$. Then $x=\frac{95\times109.5}{125}$. Calculate $95\times109.5 = 10402.5$, and $x=\frac{10402.5}{125}=83.22$ m.

Answer:

$83.22$ m