The hypotenuse of a right triangle is 1 cm more than twice the shorter leg, and the longer leg is 9 cm less than three times the shorter leg. Find the lengths of the three sides of the triangle.

dizxindlert7

dizxindlert7

Answered question

2022-09-04

The hypotenuse of a right triangle is 1 cm more than twice the shorter leg, and the longer leg is 9 cm less than three times the shorter leg. Find the lengths of the three sides of the triangle.

Answer & Explanation

Gerardo Kent

Gerardo Kent

Beginner2022-09-05Added 12 answers

The hypotenuse is 2x+1
The long side is 3x-9
Use the pythagoreum theurom:
x>2 + (3x-9)>2 = (2x+1)>2
Factor
x>2 +9x>2 -27x -27x +81 = 4x>2+4x +1
Bring itto one side
6x>2 -58x +80 =0
Use the quadratic equation and plug it in.
58 plus or minus radical 58>2 -4 times 6 times 80 ALL over2 times 6
Simplify
58 plus or minus radical 3364-1920 ALL over 12
The two thousands numbers equal 1444. Radical 1444 is 38
58 plus or minus 38 ALL over 12
x = 8
The short side is 8
The long side is 15
The hypotonuse is 17

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