the difference between the length of a hypotenuse and the length of the next longest side of a right triangle is 3 cm. the difference between the lengths of the two perpendicular sides is 3cm. find the three side lengths

Question

anonymous · Answer

would someone please explain how i answer the question?

directrix · Answer

I think I know how to do this but I have to help someone finish a problem.

Let h be the hypotenuse. Then, H = 3 + L-one where L-one is the longer leg.

Let L-two = L-one minus 3 because L-two is the shorter of the two legs.

The equation (Pythagorean Theorem) would be:

h^2 =( Leg1)^2 + (Leg2)^2

(3 + L1)^2 = ( Leg1)^2 + (Leg2)^2

(3 + L1)^2 = ( Leg1)^2 + (3 + L1)^2

Now, solve for Leg One as denoted by L1. First, see if you agree with the equation.

directrix · Answer

Do you understand the equation?

anonymous · Answer

so shouldn't it be  (3+L1)^2 = (leg 1)^2 + (L1 - 3)^2
?? :S

campbell_st · Answer

|dw:1333912776340:dw|

then its x^2= (x - 6)^2 + (x - 3)^2

x^2 = x^2 - 12x + 36 + x^2 - 6x + 9

collect like terms and simplify

x^2 - 18x + 45 = 0

(x - 15)(x - 3) = 0

x = 15, 3

the solution of x = 3 can't be used as the side lengths would be  x=3, 0 and -3

use x = 15

Hypotenuse = 15, shorter side = 12 shortest side = 9  ( 3,4,5 triad)