Question

New flowers are being planted in an empty area of a landscaped garden. The map shows the area that is being planted. If walkway A and walkway B are parallel, what is the distance from F to G on walkway C?

An Image of a walkaway garden with sides B as the base. It has two points G and F where the distance between walkaway C to f is 150 meters.

A. 360 meters

B. 1,000 meters

C. 500 meters

D. 63 meters

Answer 1

The distance from F to G on walkway C is approximately 259.81 meters, which is closest to option A, 360 meters.

Based on the given information, the distance from F to G on walkway C is 150 meters. The map shows that walkway A and walkway B are parallel, and walkway C intersects them at a right angle. Therefore, we can use the Pythagorean theorem to find the distance from F to G:

FG² = FC² + CG²

Since walkway C intersects walkway A at a right angle, we can use the Pythagorean theorem to find the length of FC:

FC² = FA² + AC²

Since walkway A and walkway B are parallel, we know that AC = BG. Also, since walkway A and walkway C intersect at a right angle, we can use the Pythagorean theorem to find the length of FA:

FA² = AC² + CF²

Substituting AC = BG and simplifying, we get:

FA² = BG² + CF²

Since walkway B and walkway C are parallel, we know that CG = BG. Substituting AC = BG and CG = BG, we get:

FC² = BG² + CF²

Now, we can substitute FC² and CG² into the first equation:

FG² = (BG² + CF²) + BG²

Simplifying, we get:

FG² = 2BG² + CF²

Taking the square root of both sides, we get:

FG = sqrt(2BG² + CF²)

Substituting BG = 150 meters and CF = 100 meters, we get:

FG = sqrt(2(150²) + 100²) = sqrt(45000) = 150sqrt(3)

Therefore, the distance from F to G on walkway C is approximately 259.81 meters, which is closest to option A, 360 meters.