anonymous
  • anonymous
find the length of shorter leg of a right triangle if the longer leg is 20feet more than the shorter leg and the hypotenuse is 20feet less than twice the shorter. please explain this whole thing to help me solve it.
Differential Equations
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
it helpes to set the shorter leg to x. so you get that the longer leg L = x + 20 and you get that the hypotenuse H = 2x - 20 now use that it is a right triangle so that x^2 + L^2 = H^2 and fill in H and L with the x's then solve for x and get the length of the shorter leg
anonymous
  • anonymous
The problem provides you with three equations. Let's say that the shorter leg is called A, the longer leg is called B, and the hypotenuse is C. Because it's a right triangle, we know that A^2 + B^2 = C^2. We know that the longer leg is 20 feet more than the shorter leg, so B = A + 20. We know that the hypotenuse is 20 feet less than twice the shorter leg, so C = 2A - 20. Writing all these out gives us a system of equations: A^2 + B^2 = C^2 B = A + 20 C = 2A - 20. The second two equations give use expressions for B and C in terms of A. We can substitute these into the first equation to reduce it to an equation of only a single variable, A: A^2 + (A+20)^2 = (2A-20)^2 Simplifying: A^2 + A^2 + 40A + 400 = 4A^2 - 80A + 400 2A^2 + 40A = 4A^2 - 80A. 120A = 2A^2. A^2 = 60A. A = 60. Now we can substitute this value into our other two equations: B = A + 20 = 60 + 20 = 80 C = 2A - 20 = 2* 60 - 20 = 100. (A,B,C) = (60,80,100).
anonymous
  • anonymous
@stoopkid Don't completely solve the question. I thinkt that this person is genuine but don't give the full answer away ;)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
thank u i was stuck at where 120 came from thank u

Looking for something else?

Not the answer you are looking for? Search for more explanations.