Question

The difference between the sides of a right angle 🔺 containing the right angle 7 CM and it's area 60cm .Find perimeter

Answer 1

Let one side at right angle be x
the other must be x-7

area of a triangle =(1/2) × (height) (base)
60 = (1/2)(x)(x-17)
60 = (x^2 -7x)/2
120 = x^2 -7x

x^2 -7x -120 = 0
x^2 -15x +8x -120 =0
x (x-15) + 8 (x-15) =0
(x-15)(x+8)=0

now, find x
x-15 =0
x = 15

again
x+8 =0
x = -8

as the side couldn't be -v so the value of x as a side must be 15cm

so the measure of one side we got is x =15cm and the other side = x-7 = 15 -7 =8cm

apply pythagoras theorem for third side as it is a right angled triangle

[let hypotaneous be a]

(15)^2 + (8^2) = a^2
225 +64 = a^2
289 = a^2
a = 17 cm

so the hypataneous = 17cm

perimeter of a triangle = sum of all sides
= (15+ 8 + 17 ) cm
= 40 cm
Hope you understand