Question

to indirectly measure the distance across a lake, bilquis makes use of a couple landmarks at points m and n. she measures lo, om, and op as marked. find the distance across the lake (mn), rounding your answer to the nearest hundredth of a meter. (diagram is not to scale.) 115 m 104.55 m 140 m answer attempt 1 out of 2 mn =

Explanation:

Step1: Use similar - triangles property

Since $\triangle LOP\sim\triangle LMN$ (by AA similarity, as the angles at $L$ are common and the right - angles are equal). The ratios of corresponding sides of similar triangles are equal. That is, $\frac{LO}{LM}=\frac{OP}{MN}$.
We know that $LO = 140$ m, $LM=140 + 115=255$ m, and $OP = 104.55$ m.

Step2: Solve for $MN$

From $\frac{LO}{LM}=\frac{OP}{MN}$, we can cross - multiply to get $MN=\frac{OP\times LM}{LO}$.
Substitute the values: $MN=\frac{104.55\times255}{140}$.
First, calculate $104.55\times255 = 104.55\times(200 + 50+5)=104.55\times200+104.55\times50 + 104.55\times5=20910+5227.5 + 522.75 = 26660.25$.
Then, $\frac{26660.25}{140}\approx190.43$ m.

Answer:

$190.43$ m