Math, asked by yogi251079, 11 months ago

Two legs of a right triangle are of lengths 12 cm and 5
cm, the length of the side of the largest square that can
be inscribed in the triangle is​

Answers

Answered by Agastya0606
0

Given: Two legs of a right triangle are of lengths 12 cm and 5 cm.

To find: The length of the side of the largest square that can  be inscribed in the triangle=?

Solution:

  • Now, as the triangle is right angled, so let the side of the square inscribed in the triangle be x.
  • the remaining height will be 12 - x and the rest base will be 5-x.
  • Now the triangles formed after the construction of the square will be similar.
  • So,

                x / ( 12 - x ) = ( 5 - x ) / x

  • By cross multiplication, we get:

                x² = ( 5 - x ) x ( 12 - x )

                x² = 60 - 5x - 12x + x²

  • cancelling x² from both sides, and taking - 5x - 12x in LHS, we get:

                17x = 60

                x = 60/17 cm

Answer:

                  So the length of the side of the largest square that can  be inscribed in the triangle is​ 60/17 cm

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