Question

The sides of a triangle are 5 12 13 . A square was constructed in the triangle such that two sides of triangle coincides with the sides of the square . What is the area of square?

Answer 1

Answer:

12.45

Step-by-step explanation:

The sides of a triangle are 5 12 13 . A square was constructed in the triangle such that two sides of triangle coincides with the sides of the square . What is the area of square?

Triangle with sides 5 , 12 & 13 is a right agle trianngle

as 5² + 12² = 13²

Where 5 & 12 are at right angles

Square will be on Side of 5 & 12

now if side of square = x

then  triangles will be formed with 5-x  & x side   or  x & 12 - x

which will be similar to original triangle

=> 12/5  = x/5-x        or  12/5 = 12-x/x

=> 60 - 12x = 5x

=> 17x = 60

=> x = 60/17

Area of square = (60/17)² = (3.53)² = 12.45