Question

A triangle whose three in two sides are equal 12 and its perimeter is 30cm . Find its area ​

Answer 1

Step-by-step explanation:

of isosceles triangle=30cm

Length of equal sides=12cm

Let third side of triangle=xcm

According to problem,

x+12+12=30

x+24=30

x=30−24

x=6

∴ Third side of triangle=6cm

Using Heron's formula

Area of triangle=

s(s−a)(s−b)(s−c)

sq. units

where s=

2

a+b+c

s=

2

30

=15

Area of triangle=

15(15−12)(15−12)(15−6)

cm

2

=

15×3×3×9

cm

2

=3×3×

15

cm

2

=9

15

cm

2

∴ Area of triangle=9

15

cm

2

.

Answer 2

Perimeter of isosceles triangle=30cm

Length of equal sides=12cm

Let third side of triangle=xcm

According to problem,

x+12+12=30

x+24=30

x=30−24

x=6

∴ Third side of triangle=6cm

Using Heron's formula

Area of triangle=

$Area of triangle=s(s−a)(s−b)(s−c) sq. units//where s=2a+b+c//s=230=15//Area of triangle= \sqrt{15(15−12)(15−12)(15−6)cm2} //= \sqrt{15×3×3×9cm2} //= 3×3× \sqrt{15cm2} //=9 \sqrt{15cm2} //∴ Area of triangle=9 \sqrt{15cm2.} </p><p>$