Question

Area of the triangle having perimeter 30 cm, one side 12 cm and difference of other two sides as 2 cm is​

Answer 1

Step-by-step explanation:

One side =12

Let the other side be x

And another x+2

Perimeter =30

A/q,

x+x+2+12=30

2x=30-14

2x=16

x=16/2

x=8

The other 2 side 8 cm and (8+2)=10 cm

Therefore

Semi perimeter =8+10+12=30/2=15

According to the Herons formula

Answer 2

Answer:

The area is 15√7 sq.cm

Step-by-step explanation:

One side = 12 cm

Difference between 2 sides = 2 cm

Perimeter = 30 cm

Let one side be x and other is (2 - x)

Perimeter of triangle = Sum of all sides

                             30 = 12 + x + (2 + x)

                             30 = 14 + 2x

                      30 - 14 = 2x

                              2x = 16

                                x = 16/2

                                x = 8

One side = 8cm ; Other side = (x + 2) = 8 + 2 = 10 cm

Area of triangle by heron's formula,

Semi perimeter = 30/2 = 15 cm

Area = √[s(s - a)(s - b)(s - c)]

        = √[15(15 - 12)(15 - 8)(15 - 10)]

        = √[15 * 3 * 7 * 5]

        = √[5 * 3 * 3 * 7* 5]

        = 5*3√7

        = 15√7 sq. cm

The area is 15√7 sq.cm