Use the image to answer the question.
A rectangle is formed from two right triangles. The base of the rectangle measures 80 yards and is labeled Johnson Avenue. The top of the rectangle is labeled Edison Avenue. The left side joining both the avenues is labeled 41st street and measures 60 yards. The right side of the rectangle is labeled 42nd street. A bank is located at the vertex of 41st street and Edison Avenue. The hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street is labeled park.
Yasin likes to walk to work when the weather is nice. He works at the bank at the corner of 41st Street and Edison Avenue. His house is at the corner of 42nd Street and Johnson Avenue. Assuming that the street intersections are 90° angles, how far does Yasin need to walk if he goes through the park to work? Round your answer to the nearest tenth, if necessary.
(1 point)
Responses
100 yd.
100 yd.
10,000 yd.
10,000 yd.
52.9 yd.
52.9 yd.
11.8 yd.
To find the distance Yasin needs to walk if he goes through the park, we need to find the length of the hypotenuse of the right triangle formed by the park, 41st Street, and Edison Avenue.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
a^2 + b^2 = c^2
In this case, the lengths of the two legs of the triangle are 60 yards (41st Street) and 80 yards (Johnson Avenue). Plugging these values into the equation, we get:
60^2 + 80^2 = c^2
3600 + 6400 = c^2
10000 = c^2
Taking the square root of both sides, we find:
c = √10000
c = 100
Therefore, Yasin needs to walk 100 yards if he goes through the park to work.