10

Legs ( sides other than the hypotenuse) of a right triangle are of lengths 12 and 6 cm. Find the side of the largest square that can be inscribed in the triangle.?

  1. 👍 0
  2. 👎 0
  3. 👁 172
asked by ritu
  1. Geometry?

    If you follow directions and put your School Subject in the School Subject box, you're more likely to get the right kind of help sooner.

  2. Nice problem.

    Let
    ABC be the right-triangle, right-angled at C, such that AC=12, BC=6.
    Let the "inscribed" square share a common right-angle at C, and meet the hypotenuse AB at D.

    Let E be a corner of the square on AC, and F be a corner of the square on BC.

    Let x denote the side length of the square.

    Then ΔADE is similar to ΔDBF.

    By the ratio of the sides, we have
    x/(12-x)=(6-x)/x
    Cross multiply and solve for x to get
    x=4.

    1. 👍 0
    2. 👎 0
    posted by MathMate
  3. What happens if the square does not share sides with the triangle?

    If the vertices of the triangle are at (0,0),(6,0),(0,12), then if one side of the square is on the hypotenuse, and one corner is at (s,0), another is at (0,2s), so the hypotenuse has length √5 s.

    Now, we also know that

    s + √(5s^2 + 5/4 s^2) = 6
    s = 12/7
    and the square has side

    x = 12/7 √5 = 3.83

    Hmmm. It appears that MathMate has found the maximal square. We'd have to consider the square at various angles of rotation, and find the angle which maximizes its area. I suspect it is indeed such that the square and the triangle share the right angle.

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. geometry

    Given the hypotenuse of a right triangle is 600, and the length of all three sides is 1400, what are the lengths of the legs?

    asked by Cori on January 22, 2012
  2. Math Help!

    The radius of this circle is one unit. Find the exact lengths of the legs in the right triangle if: Sides a is twice as long as side b. And Sides b is twice as long as side a. Basically the hypotenuse of this triangle is 1 and we

    asked by David on December 12, 2015
  3. Math Help Please

    The radius of this circle is one unit. Find the exact lengths of the legs in the right triangle if: Sides a is twice as long as side b. And Sides b is twice as long as side a. Basically the hypotenuse of this triangle is 1 and we

    asked by David on December 12, 2015
  4. Math

    The radius of this circle is one unit. Find the exact lengths of the legs in the right triangle if: Sides a is twice as long as side b. And Sides b is twice as long as side a. Basically the hypotenuse of this triangle is 1 and we

    asked by David D. on December 12, 2015
  5. Algebra

    Which statement about a right triangle is NOT true? A.) The hypotenuse is the longest side of the triangle. B.) The square of the hypotenuse is equal to the sum of the squares of the other two lengths. C.) The sum of the length of

    asked by Elizabeth on February 10, 2020
  1. Math

    If the hypotenuse of a right triangle is 13 and one of its legs is 5, find the area fo the triangle. Answer Choices 20 40 45 30 25 I know a hypotenuse the side of a right triangle opposite the right angle. You can't multiply the

    asked by Sahana Epari on August 20, 2009
  2. math

    The legs of a right triangle are 3 and 4 units long. Find the lengths, to the nearest tenth, of the segments into which the bisector of the right angle divides the hypotenuse. (Hint: Draw a picture of the triangle, label one

    asked by molly on June 8, 2012
  3. Math Help Please

    1. Which set of numbers represents a Pythagorean triple? 6, 9, 12 7, 10, 12 16, 18, 25 27, 36, 45 ** 2. If the lengths of the legs in a right triangle are 7 and 8, what is the approximate length of the hypotenuse? 1.4 3.8 5.4 10.6

    asked by Pueblo on November 28, 2016
  4. Math PLZZ

    1. Which set of numbers represents a Pythagorean triple? 6, 9, 12 7, 10, 12 16, 18, 25 27, 36, 45* 2. If the lengths of the legs in a right triangle are 7 and 8, what is the approximate length of the hypotenuse? 1.4 3.8 5.4* 10.6

    asked by YOLO on October 21, 2015
  5. Math

    If all of the following triangles have the same perimeter, which has the greater area? a) a right triangle with legs of equal lengths b) an equilateral triangle, c) An obtuse triangle d) a triangle whose sides are all different

    asked by Anonymous on August 8, 2012

More Similar Questions