Find the perimeter and area of a triangle whose sides are of lengths 52 cm, 56 cm and 60 cm respectively.

Options

A. 1344 `cm^(2)`
B. 1444 `cm^(2)`
C. 1544 `cm^(2)`
D. 1644 `cm^(2)`

Answer

A

Explanation

Let a = 52 cm, b = 56 cm and c = 60 cm.
Perimeter of the triangle = (a + b + c) units
= (52 + 56 + 60)cm = 168 cm.
`therefore" "s=(1)/(2)(a+b+c)=((1)/(2)xx168)cm = 84 cm`.
`therefore" "(s-a)=(84-52)cm = 32 cm, (s-b)=(84-56)cm = 28 cm and (s-c)=(84-60)cm = 24 cm`.
By Heron's formula, the area of the given triangle is
`Delta = sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(84 xx 32 xx 28 xx 24) cm^(2)`
`=sqrt(14 xx 6 xx 16 xx 2 xx 14 xx 2 xx 6 xx 4)cm^(2)`
`=(14 xx 6 xx 4 xx 2 xx 2)cm^(2)=1344 cm^(2)`
Hence, the area of the given triangle is 1344 `cm^(2)`.