Question

sum of the perpendicular sides of a right angled triangle is 42 cm. if it's hypotenuse is 30 cm find the lengths of the perpendicular sides​

Answer 1

Answer:

a= 24 , c = 18

Step-by-step explanation:

Let the length of the sides be a,b,c where b is hypotenuse, so we get,

a+ c = 42 ,

given,

b = 30

We know that, b² = a² + c²

we get, 900 = (a+c) ² – 2ac

900 = 1764 – 2ac

ac = 432

we know that,

(a-c)² = (a+c)² - 4ac

(a-c)² = 1764 - 1728

(a-c)² = 36

so, a - c = 6 and a + c = 42

By solving the two equations we get, a = 24 , c = 18