Question

area of a right triangle is 24 cm square and the square of the sum of the perpendicular sides is 196. Find the lengths of sides of the triangle​

Answer 1

Answer:

8 cm & 6 cm

Explanation:

Let the sides are 'a' and 'b'. (a>b)

Square of sum of the perpendicular sides is 196.

=> (a + b)² = 196

=> a + b = √196 = 14

=> b = 14 - a ... (1)

Area = 24 cm²

=> 1/2 *height * base = 24 cm²

=> 1/2 *a * b = 24

=> ab = 48

=> a(14 - a) = 48 {from (1)}

=> 14a - a² = 48

=> a² - 14a + 48 = 0

=> a² - 8a - 6a + 48 = 0

=> (a - 8)(a - 6) = 0

=> a = 8 & a = 6,

Take a = 8, as we took a>b, if a = 6 then b = 14-6=8 which is greater than 6.

So a = 8 then b = 14 - 8 = 6