A rake is leaning against a wall. The top of the rake hits the wall 63 inches above the ground and the bottom of the rake is 16 inches away from the base of the wall. A beetle crawls from the bottom of the rake to the top of the rake. Then the beetle climbs down to the base of the wall and back to the bottom of the rake. How far does the beetle travel in all? _____ inches

Question

A rake is leaning against a wall. The top of the rake hits the wall 63 inches above the ground and the bottom of the rake is 16 inches away from the base of the wall. A beetle crawls from the bottom of the rake to the top of the rake. Then the beetle climbs down to the base of the wall and back to the bottom of the rake. How far does the beetle travel in all?  _____ inches

Bytelearn · Accepted Answer

Question Prompt:  question_prompt: How far does the beetle travel in total?Identify Triangle Components:  Identify the legs and hypotenuse of the right triangle formed by the rake and the wall. Legs: 63 inches (height), 16 inches (base) Hypotenuse: x (length of the rake)Use Pythagorean Theorem:  Use the Pythagorean Theorem to find the length of the rake. a^2 + b^2 = c^2 63^2 + 16^2 = x^2Calculate Squares:  Calculate the squares of the legs. 63^2 = 3969 16^2 = 256Add Squares:  Add the squares of the legs to find the square of the hypotenuse. 3969 + 256 = x^2 x^2 = 4225Find Rake Length:  Take the square root of both sides to find the length of the rake. sqrt(x^2) = sqrt(4225) x = 65Calculate Total Distance:  Calculate the total distance the beetle travels. Distance up the rake: 65 inches Distance down the wall: 63 inches Distance along the ground: 16 inches Total distance = 65 + 63 + 16Add Distances:  Add up the distances to get the total distance traveled by the beetle. Total distance = 65 + 63 + 16 = 144 inches

Full solution

More problems from Pythagorean Theorem and its converse

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