Question

The equal sides of the
isosceles triangle are 12 cm, and the perimeter is 30cm. The
area of this triangle is
​

Answer 1

Answer:

In the above formula, “s” represents the semi – perimeter of the triangle, “a, b and c” represents the sides of the triangle ABC. Perimeter of the triangle is given as 30 cm so the semi perimeter is equal to half of the perimeter i.e. 15 cm. Hence, the area of the triangle is equal to 9√15cm2.

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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=

s(s−a)(s−b)(s−c)

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