Question

12. The sides of a triangle are given by x, 2x + 2 and 3x – 2. If its perimeter is 30 cm,
then find the smallest side of the triangle.
13. Find the breadth of a rectangle with length 15 metres and area 165 sq. metres.
14. The angles of a triangle are x.​

Answer 1

Answer:

If a,b,c are the sides of a triangle , then according to Hero's Formula area of triangle is

s(s−a)(s−b)(s−c)

where s=

2

a+b+c

For the given triangle,

s=

2

x+x+1+2x−1

=

2

4x

=2x

Area =x

10

2x(2x−x)(2x−x−1)(2x−2x+1)

=x

10

2x(x)(x−1)(1)

=x

10

x

2(x−1)

=x

10

2(x−1)

=

10

⇒2(x−1)=10

x−1=5

x=6