Question

the perimeter of a right angled triangle is 72 cm and its area is 216 cm square .find the sum of the lengths of its perpendicular sides ( in cm).​

Answer 1

Step-by-step explanation:

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