Question

The area of a triangle is 72 cm and the three altitude measures 24 cm, 18 cm, 16 cm. Find the perimeter of the triangle. ​

Answer 1

Answer:

REF.Image

Perimeter of right triangle = 72

a+b+c= 72 _____________ (1)

its area = 216

2

1

ba=216

ba=432 ___________ (2)

∴c

2

=a

2

+b

2

(By pythagoras theorem )

(a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ac

(72)

2

=c

2

+c

2

+2ab+2bc+2ac

5184=2c

2

+2ab+2bc+2ac

5184=2c

2

+2ab+2c(b+a)

5184=2c

2

+2ab+2c(72−c)

5184=2c

2

+2ab+144c−2c

2

5184=2ab+144c

5184=2×432+144c

c=

144

9320

c=30

putting c in equation (1)

a+b+c=72

a+b=72-30

a+b=42.