Question

The perimeter of a right angled triangle is 48 centimetres and its area is 96 square centimetres. Length of the hypotenuse is 20 centimetres

What are the lengths of the perpendicular sides ?​

pls help

Answer 1

Answer:

16 and 12

Step-by-step explanation:

let say those sides are a, b, c

and c is the hypotenuse

so c=20

so perimeter =a+b+c=48

a+b +20=48

a+b=48-20=28

a+b=28---eq1

and area of a right triangle = 1/2 * product of two perpendicular lines, in this case a and b

1/2ab=96

ab= 96*2= 192

we know a+b and ab

in order to find a-b use

(a+b)^2-4ab= (a-b) ^2

so

28^2-4*192=(a-b) ^2

784-768= (a-b) ^2

(a-b) ^2=16

so a-b =4---eq2

from eq1 and eq2

a+b=28

a-b=4

add both of them

2a=32

a=16

so b= 12