The lengths of the sides of a right triangle are x-1, x, x+8. Find the

1.	The lengths of the sides of a right triangle are x-1, x, x+8. Find the numeric value of the perimeter of the triangle.
Answer» Answer: 67 Step-by-step EXPLANATION: Пусть ΔАВС-прямоугольный , ∠С=90. Тогда гипотенуза АВ=х+8 ( наибольшая) . Катеты СА=х-1 ,СВ=х. По т. Пифагора АВ²=СА²+СВ² , (х+8)²=(х-1)²+х² , х²+16х+64=х²-2х+1+х² , х²-18х-63=0 ,D=324+252=576=24² x=20 , х=-4 –не подходит по смыслу задачи. АВ=20+8=28 , СА=20-1=19 , СВ=20. Р=28+19+20=67

The lengths of the sides of a right triangle are x-1, x, x+8. Find the numeric value of the perimeter of the triangle.

Answer»

Answer:

Step-by-step EXPLANATION:

Пусть ΔАВС-прямоугольный , ∠С=90. Тогда гипотенуза АВ=х+8 ( наибольшая) . Катеты СА=х-1 ,СВ=х.

По т. Пифагора АВ²=СА²+СВ² ,

(х+8)²=(х-1)²+х² ,

х²+16х+64=х²-2х+1+х² ,

х²-18х-63=0 ,D=324+252=576=24²

x=20 , х=-4 –не подходит по смыслу задачи.

АВ=20+8=28 ,

СА=20-1=19 ,

СВ=20.

Р=28+19+20=67

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The lengths of the sides of a right triangle are x-1, x, x+8. Find the numeric value of the perimeter of the triangle.

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