one leg of a right triangle is 1cm longer than the other leg, and hypothenuse is 2cm longer than the shorter leg. find the lengths of the three sides of the triangle.
2006-11-22 23:30:29 · 3 answers · asked by khamyll 1 in Science & Mathematics ➔ Mathematics
Let the shorter leg be 'x'
Longer leg = 'x + 1'
Hypotenuse = 'x + 2'
x^2 + (x + 1)^2 = (x + 2)^2
x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
2x^2 + 2x + 1 = x^2 + 4x + 4
x^2 + 2x + 1 = 4x + 4
x^2 -2x - 3 = 0
x^2 + x - 3x - 3 = 0
x(x + 1) -3(x + 1) = 0
(x - 3)(x + 1) = 0
Either x - 3 or x + 1 = 0
If x + 1 = 0, x = -1 which cannot be true for the triangle
If x - 3 = 0, x = 3
Therefore, the sides are:
Shorter leg = 3cm
Longer leg = 3 + 1 = 4cm
Hypotenuse = 3 + 2 = 5cm
2006-11-23 02:15:07 · answer #1 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 0⤋
Let x be length of short leg
x+1 = length of long leg
x+2 = length of hypotenuse
By Pythagorean theorem:
hypotenuse^2 = (short leg)^2 + (long leg)^2
The equation is: (x+2)^2 = x^2 + (x+1)^2
one equation, one unknown...solve for x
2006-11-23 07:42:58 · answer #2 · answered by Chris 2 · 2⤊ 0⤋
shorter leg=2
hypothenuse=4
the other leg=3
2006-11-25 09:25:14 · answer #3 · answered by kittaaaay 2 · 0⤊ 0⤋