Question

What is the area of a triangle having perimeter 32cm, one side 11cm and difference of other two sides 5cm?

• A. $$8\sqrt{30}sqcm$$
• B. $$5\sqrt{35}sqcm$$
• C. $$6\sqrt{30}sqcm$$
• D. $$8\sqrt{2}sqcm$$

Answer 1

Answer:

$$8\sqrt{30}sqcm$$

Let the sides of triangle be a, b and c respectively.

2s = a + b + c = 32

11 + b + c = 32

b + c = 32 – 11 = 21 .....(i)

and b – c = 5 ......(ii)

By adding equations (i) and (ii)

2b = 26

b = 13

c = 13 – 5 = 8

Now, 2s = 32

s = 16

a = 11, b = 13, c = 8

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

$=\sqrt{16(16-11)(16-13)(16-8)}$

$=\sqrt{16\times{5}\times{3}\times{8}}$

$=8\sqrt{30}$sq.cm