Q. 704.3( 9 Votes )

The length of the hypotenuse of a right – angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.

Answer :

Let the base and altitude of the right angled triangle be x and y respectively.

Thus the hypotenuse of triangle will be x + 2 cm


(x + 2)2 = y2 + x2 – – – (1)


Also the hypotenuse exceeds twice the length of the altitude by 1 cm


h = 2y + 1


x + 2 = 2y + 1


x = 2y – 1


Putting the value of x in (1) we get


(2y – 1 + 2)2 = y2 + (2y – 1)2


(2y + 1)2 = y2 + 4 y2 – 4y + 1


4y2 + 4y + 1 = 5y2 – 4y + 1 using (a + b)2 = a2 + 2ab + b2


– y2 + 8y = 0


y(y – 8) = 0


y = 8


x = 16 – 1 = 15cm


h = 16 + 1 = 17cm


Thus the base, altitude, hypotenuse of triangle are 15cm, 8cm, 17cm respectively.


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