Question

Find the area of a triangle if the sides are in the ratio 2:2:3 and its semiperimeter is 21cm​

Answer 1

Data

Semi perimeter = 21 cm

perimeter = 42 cm

FORMULA PART

(Let the ratios be summed up)

ATQ.

Let the number be x

2x+2x+3x = 7x

here

7x = perimeter

7x=21cm

x=3 cm

2x = 6cm

3x=9cm

now apply Heron's formula

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

here A,B,C ARE THE SIDES

a= 6cm

b= 6cm

c=9cm (we just calculated above Heron's formula)

s(semi perimeter) = 21cm

$\sqrt{21 (21-6)(21-6)(21-9)}\\=\sqrt{21 (15)(15)(12)} \\=90\sqrt{7}cm^{2}$

or 90  x root of 7 =238.117 $cm^{2}$