A triangular face of the roof of the garage has two sides that are StartRoot 93 EndRoot feet in length each and a base of length StartRoot 186 EndRoot feet. Is the roof a right triangle? Explain the steps to take to determine whether the roof forms a right triangle.
Answers
Given:
A triangular face of the roof of the garage has two sides that are StartRoot 93 EndRoot feet in length each and a base of length StartRoot 186 EndRoot feet.
To find:
To determine whether the roof forms a right triangle
Solution:
Using Pythagorean triplets a² + b² = c², let us consider the 2 cases.
Case I
(√93)² + (√186)² = 279
⇒ c² = 279
∴ c = √279 = 16.7
as, 279 is not a perfect square, the roof cannot forma a right triangle.
Case II
(√93)² + b² = (√186)²
93 + b² = 186
⇒ b² = 186 - 93
⇒ b² = 93
∴ b = √93 = 9.64
as, 93 is not a perfect square, the roof cannot forma a right triangle.
Answer:
First, identify the longest length, the square root of 186, as the hypotenuse. Find the squares of each side. For the roof, the sum of the squares of the two shorter sides, 186, equals the square of the longest side, 186. Yes, the roof is a right triangle.
Step-by-step explanation:
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