Question

Half of the perimeter of a triangle is 20 cm. The product of (s-a), (s-b) and (s-c) is 20 cubic cm, where s = a + b + c, then area of triangle is equal to *

Answer 1

Answer:

20 cmsq.

Step-by-step explanation:

we know that

area of a triangle(by heron's formula)= √s (s-a)(s-b)(s-c)

area= √20×20

area= √ 400

area= 20 cm Sq.

Answer 2

Half of the perimeter of a triangle is 20 cm.

The product of (s-a), (s-b) and (s-c) is 20 cm³, where s = a + b + c.

We have to find, Area of triangle?

━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

Area of triangle is given by,

$\maltese\;{\boxed{\sf{\pink{A = \sqrt{s(s - a)(s - b)(s - c)}}}}}\qquad\qquad\bigg\lgroup\bf Heron's\;Formula \bigg\rgroup$

where,

s = semi perimeter

$\dashrightarrow\sf s = 20\;cm$

we have,

$:\implies\sf (s - a)(s - b)(s - c) = 20\;cm^2$

Now Putting value,

$:\implies\sf A = \sqrt{20\;cm \times 20\;cm^3}$

$:\implies\sf A = \sqrt{400\;cm^4}$

$:\implies{\boxed{\sf{\purple{A = 20\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\; triangle\;is\; \bf{20\;cm^2}.}}}$