# The perimeter of a right triangle is 72 cm and its area is 216 cm2. Find the sum of the lengths of its perpendicular sides. (in cm)

The Sum of length of perpendicular sides is 42 cm

1) Let the base of triangle be a, height be b and hypotenuse be c.

2) Given a + b+c = 72 cm and ab/2 = 216 or ab =432

3) Squaring the first equation

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

4) Using Pythagorean Equation

72² = c²+c²+2(ab+bc+ca)

5184 = 2c²+2(ab+c(a+b))

2592 = c²+ ab + c(a+b)

2592 = c² + 432 +c(a+b)

2160 = c² +c(a+b)

5) Taking c common on RHS

2160 = c(a+b+c)

2160 = c*72

c= 30 cm

6) Substituting in the first equation, a+b = 42 cm

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DEAR STUDENT ,

The Sum of length of perpendicular sides is 42 cm ..............

STEP :1) Let the base of triangle be a, height be b and hypotenuse be c.

STEP :2) Given a + b+c = 72 cm and ab/2 = 216 or ab =432

STEP :3) Squaring the first equation

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

STEP :4) Using Pythagorean Equation

72² = c²+c²+2(ab+bc+ca)

5184 = 2c²+2(ab+c(a+b))

2592 = c²+ ab + c(a+b)

2592 = c² + 432 +c(a+b)

2160 = c² +c(a+b)

5) Taking c common on RHS

2160 = c(a+b+c)

2160 = c*72

c= 30 cm

STEP :6) Substituting in the first equation, a+b = 42 cm ANS  ....