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
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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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