algebra

The hypotenuse of a right triangle is 8m long. One leg is 2m longer then the other. Find the lengths of the legs. How would you solve this equation?

  1. 👍 0
  2. 👎 0
  3. 👁 71
asked by Lexi
  1. short leg --- x
    longer leg --- x+2

    x^2 + (x+2)^2 = 8^2
    x^2 + x^2 + 4x + 4 - 64 = 0
    2x^2 + 4x - 60 = 0
    x^2 + 2x - 30 = 0
    let's complete the square:
    x^2 + 2x + 1 = 30+1 = 31
    (x+1)^2 = 31
    x+1 = ± √31
    x = -1 ± √31
    but x has to be positive,
    so x = √31 - 1 = appr 4.568

    so one side is 4.568, the other is 6.568

    check:
    4.568^2 + 6.568^2 = 64.0052
    close enough to 64

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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.

    asked by Anneliese on January 23, 2017
  2. algebra

    One more triangle question,please. In this triangle,the short leg is x and the longer leg is 1/2x + 11. If the hypotenuse is 2x + 1, what are the lengths of each side of this right triangle? Please show all calculations. Short leg

    asked by Anneliese on January 23, 2017
  3. Math

    Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the

    asked by Jerry on December 29, 2015
  4. Algebra II

    In a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg. A). If the shorter leg is representd by x, write

    asked by Austin on October 28, 2018
  5. Algebra

    A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?

    asked by Jennifer on April 22, 2011
  6. Algebra 2 Honors

    Hi, I'd like some help with one of the questions on my math homework. It has to do with a right triangle. I'm not sure how to set it up or if I should use the pythagorean theorem. This is the question: Vista county is setting

    asked by Spectrum on March 1, 2015
  7. Math

    The length of the hypotenuse of a right triangle is 2m more than the longer leg. The longer leg is 7m longer than the shorter leg. Find the perimeter of the triangle. ( please explain as you go)

    asked by Julia on March 31, 2016
  8. 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)

    asked by mary on September 23, 2008
  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.

    asked by Jane on April 15, 2014
  10. Math

    Right Triangle one leg is 400ft. long. The hypotenuse of the triangle is 200ft. longer than the other leg. What is the dimensions of this triangle?

    asked by Wanda on July 22, 2012
  11. algebra

    the larger leg of a right triangle is 7ft longer than its samller leg. the hypotenuse is 1ft longer than the larger leg. how many feet long is the samller leg?

    asked by jessica on March 24, 2013

More Similar Questions