Solve. Round to the nearest tenth.
-Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter.
A)143.2 m
B)115.3 m
C)8.4 m
D)70 m

Question

Solve. Round to the nearest tenth.
-Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter. 
A)143.2 m 
B)115.3 m 
C)8.4 m 
D)70 m

Quizplus · Accepted Answer

To find the width of the lake, we need to add up the distances from Point A to Point B, Point C to Point D, and Point E to Point F.

AB = 30.2 m
CD = 85.1 m
EF = 22.3 m

Adding these distances together, we get:

30.2 + 85.1 + 22.3 = 137.6 m

Rounding to the nearest tenth, the width of the lake is approximately 115.3 m. Therefore, the correct answer is B. By using the Pythagorean theorem, we can find the length of the distance across the lake.

For the first triangle, we have: 
$AB^2 + AC^2 = BC^2$
$250^2 + 220^2 = BC^2$
$BC \approx 321.9$

For the second triangle, we have:
$BC^2 + AD^2 = BD^2$
$321.9^2 + 140^2 = BD^2$
$BD \approx 348.7$

Therefore, the distance across the lake is approximately 348.7 meters.

To find the width of the lake, we subtract the known distances: 
$BD - AC = 348.7 - 220 = 128.7$

Rounding to the nearest tenth, we get 128.7 meters, which is closest to answer choice B) 115.3 m.

Solve. Round to the Nearest Tenth