Question

Two sides of a triangle is 10 cm and 12 cm. If the perimeter of the triangle is 30 cm then its third side is- *

Answer 1

Answer:8cm

Step-by-step explanation:

sides of a triangle is 10 cm and 12 cm

perimeter of the triangle is 30 cm

third side is-[ 30-(10+12)]cm=8cm

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)

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

.