SOLUTION: The length of one leg of a right triangle is 7 centimeters more than that of the other leg. the length of the hypotenuse is 3 centimeters more than double that of the shorter leg.
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Question 887877: The length of one leg of a right triangle is 7 centimeters more than that of the other leg. the length of the hypotenuse is 3 centimeters more than double that of the shorter leg. find the length of each of the three sides of the three sides.
x+7
2x+3
x Answer by 2897696(96) (Show Source):
You can put this solution on YOUR website! PART of Right TRIANGLE:
short leg: x
long leg: x+7
hypotenuse: 2x+3
we can use Pythagorean thm: a^2 +b^2 = c^2
the a &b are the legs and the c is the hypotenuse of a right triangle.
x^2 + (x+7)^2 =(2x+3)^2
x^2 +x^2+14x+49 = 4x^2+12x +9
2x^2+14x+49=4x^2+12x=9
...........0= 2x^2 -2x -4-40
...........0=2(x^2 -x -20)
...........0=2(x-5)(x+4)
........... 0=2,0=x-5,0=x+4
solve for x: 0=2 not a solution because 0 does not equal 2
...........:x=5 can be a solution
...........:x=-4 not a solution because cannot have a negative length
so..
the shortest leg length is 5 cm
long leg:
x+7
5+7
12 cm
hypotenuse:
2x+3
2(5)+3
10+3
13 cm
ANSWER: short leg: 5cm
long leg: 12cm
hypotenuse: 13 cm
use Pythagorean thm to check if it this is the correct solution
