Question

The sides of a triangle are 11m, 60m, and 61m. Find its longest altitude​

Answer 1

The area of a triangle having sides a,b,c and S as semi-perimeter is given by

A=

S(S−a)(S−b)(S−c)

S=

2

a+b+c

=

2

11+60+61

=

7

132

=66cm

We need to find the altitude to smallest side

A=

66(66−11)(66−60)(66−61)

⇒A=

66,55,6.5

⇒A=

106900

⇒A=330m

2

The area of a triangle having base AC and height P/S given by

Area (A) =

2

1

=

2

1

(Base × Height)

Area (A)=

2

1

(AC×P)

We need to find the height P. Here the smaller side is 11 m.

AC= 11 m

330=

2

1

.(11×p)

330×2=11×p

660=11×p

∴p=660/11

p=60 m.

∴ So, the answer is D. 60 m