Question

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

Answer 1

Answer: Perimeter = 168 cm; Area = 1344 cm²

Step-by-step explanation:

Perimeter = Sum of all sides = 52 cm + 56 cm + 60 cm = 168 cm

We can calculate area by using heron's formula.

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

s = semi perimeter = 168/2 = 84 cm

a = 52 cm

b = 56 cm

c = 60 cm

$\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{84(84-52)(84-56)(84-60)}$

$= \sqrt{84 \times 32 \times 28 \times 24 }$

$= \sqrt{(84) \times (32) \times (28) \times (24) }$

$= \sqrt{(2\times2\times3\times7) \times (2\times2\times2\times2\times2) \times (2\times2\times7) \times (2\times2\times2\times3) }$

$= \sqrt{2\times2\times3\times7 \times 2\times2\times2\times2\times2 \times 2\times2\times7 \times 2\times2\times2\times3 }$

$= \sqrt{2\times2\times 2\times2\times2\times2\times2 \times 2\times2\times 2\times2\times2\times3\times3\times7\times7 }$

$= \sqrt{(2\times2)\times (2\times2)\times(2\times2)\times(2 \times 2)\times(2\times 2)\times(2\times2)\times(3\times3)\times(7\times7) }$

$= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 7$

$= 64 \times 3 \times 7$

$=64 \times 21$

$= 1344$

Area = 1344 cm²

Answer 2

Step-by-step explanation:

the lengths are

• 52 cm (a)
• 56 cm (b)
• 60 cm (c)

so, the perimeter = (52+56+60) cm

= 168 cm

the half perimeter (s) = (168/2) = 84 cm.

now, the rule of the area of triangle

= √[s(s-a)(s-b)(s-c)]

so, the area = √[84(84-52)(84-56)(84-60)] cm²

= √[84×32×28×24] cm²

= √1806336 cm²

= 1,344 cm²

I hope it is a helpful answer .........