Question

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The area of a right triangle is 180 m². The height of the right triangle is 40 m. What is the length of the hypotenuse of the right triangle?

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m

Answer 1

Area of a triangle = $\frac{1}{2}$ · base x height
                     180 = $\frac{1}{2}$ · base x 40
                     180 = 20 · base
                        9  = base

Pythagorean Theorem:
base² + height² = hypotenuse²
  9²     +    40²    = hypotenuse²
 81     +   1600   = hypotenuse²
      1681            = hypotenuse²
     √1681           = √hypotenuse²
         41            = hypotenuse

Answer: the length of the hypotenuse is 41 m

Answer 2

Answer: Area of a triangle = · base x height

180 = · base x 40

180 = 20 · base

9 = base

Pythagorean Theorem:

base² + height² = hypotenuse²

9² + 40² = hypotenuse²

81 + 1600 = hypotenuse²

1681 = hypotenuse²

√1681 = √hypotenuse²

41 = hypotenuse

Answer: the length of the hypotenuse is 41 m