What is the hypotenuse of a right triangle with a base of 9 cm and an area of 54 cm2?

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问题 What is the hypotenuse of a right triangle with a base of 9 cm and an area of 54 cm²?

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答案15

解析 The area of a triangle and the length of one of the legs of a right triangle are given. However, you need the length of both legs to use the Pythagorean theorem to determine the hypotenuse. Since you have the area, start there. For a triangle, A = 1/2(base)×(height). You are given the base and area, so solve for the height:
54 =1/2(9)×(height)
height = 12
Now you know the lengths of the two legs of the right triangle and can use the Pythagorean theorem(a² + b² = c²)to determine the hypotenuse:
9² + 12² = c²
81 + 144 = c²
225 = c²
15 = c

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What is the hypotenuse of a right triangle with a base of 9 cm and an area of 54 cm2?

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Ifthelengthsoftwoofthesidesofatriangleare9and10,whichofthefollowingcouldbethelengthofthethirdside?Ⅰ.

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