Question

The sides of a triangle are 5 12 and 13.The area of the greatest square that can be inscribed in it

Answer 1

Given that the sides of a triangle are 5cm, 12cm and 13 cm .Find the area of the greatest square that can be inscribed in the triangle.

since we know that ( 5, 12 , 13 ) is a triplet of right angle triangle.

so then,base (b) = 5cm perpendicular(p) = 12cm and hypotenuse(h)=13cm

let x be the side of the greatest square that can be inscribed inside the triangle.

Find the side of square :
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in ∆ ABC

side of square

= perpendicular× base/(perpendicular + base)

x = ( p × b ) / ( p + b )

x = ( 12 × 5 ) / ( 12 + 5 )

x = 60 / 17 cm

side of square x = 60 / 17 cm

Find the area of square :
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area of square = side × side = x × x

= ( 60/ 17 ) × ( 60/ 17 ) = 3600/ 289

= 12.4 cm^2

therefore , area of the greatest square that can be inscribed in a triangle = 12.4 cm^2

Answer : area = 12.4 cm^2

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