Math

posted by .

The shorter leg of a right triangle is 14 feet shorter than the longer leg. The hypotenuse is 26 feet. How long is each leg?

  • Math -

    (X-14)^2+X^2 = 26^2
    solve for x and x-14

  • Math -

    a=shorter leg
    b=longer leg
    c=hypotenuse

    a=b-14

    c^2=a^2+b^2
    26^2=(b-14)^2+b^2
    676=b^2-2*b*14+14^2+b^2
    676=2b^2-28b+196
    676-196=2(b^2-14b)
    480=2(b^2-14b) Divide with 2
    240=b^2-14b
    b^2-14b=240
    b^2-14b+7^2=240+7^2

    Becouse: (b-7)^2=b^2-14b+7^2

    (b-7)^2=240+49
    (b-7)^2=289
    b-7=sqroot(289)

    You have two solutions:
    b-7=17 and
    b-7=-17

    Becouse sqroot(289)=+/- 17

    First solution: b-7=17
    b=17+7=24

    Second solution:
    b-7=-17
    b=17+7=-10

    leg of triangle can not be negative number so:
    b=24
    a=b-14=24-14=10

    a=10 b=24

    c=sqroot(a^2+b^2)
    c=sqroot(10^2+24^2)
    c=sqroot(100+576)
    c=sqroot(676)

    c=26

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    The hypotenuse of a right triangle is 5cm long. One leg is 3cm longer than the other leg. Find the dimensions of the shorter leg. (give your answer in radical form)
  2. intermediate algebra

    A right triangle has two legs and a hypotenuse. One leg of the triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the length of each leg. I got 12 feet and the other leg is 9 feet Is this correct?
  3. intermediate algebra

    A right triangle has two legs and a hypotenuse. One leg of the triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the length of each leg. I got 12 feet and the other leg is 9 feet Is this correct?
  4. Quadratic Equations

    The longer leg of a right triangle is 3 ft longer than three times the shorter leg. The hypotenuse is 3 ft shorter than four times the shorter leg. Find the lengths of the three sides of the right triangle. (Please provide steps/explanation …
  5. math

    did i do this right? The hypotenuse of a 30 ┬ĘC 60-90 right triangle measure 18cm. What are the lengths of the longer leg and shorter leg?
  6. Math

    A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangles be?
  7. math

    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..
  8. math

    The longer leg of a right triangle is 3 more than the shorter leg. The Hypotenuse is 6 more than the shorter leg. If the perimeter of the triangle is 36, find the length of each side of the right triangle. [ Only an algebraic solution …
  9. Math

    The longer leg of a triangle is one foot less than twice the shorter leg. The hypotenuse is 17 feet long. Find the area of the triangle.
  10. algebra

    Please show solution to this problem. In triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg. Find the lengths of each side of this right triangle. Show all calculations. Short …

More Similar Questions