Question

Please answer the 4th question

Answer 1

One side of the triangle is 11 cm.

Let the other side be x.

The difference between the third side and x is 5.

So if y is the third side:

y-x=5

=y=5+x.

Hence the three sides are x,x+5,11

Add the sides to get perimeter.

x+x+5+11=32

==) 2x+16=32

==) 2x=32-16

==) 2x=16

==) x=16/2

==) x=8

The value of x is 8.

Area of a triangle by Heron's formula is :

$\sqrt{s(s-a)(s-b)(s-c)}$

s=semiperimeter

=a+b+c/2

=8+13+11/2

=32/2

=16

Hence Area:-

$\implies \sqrt{ 16(16-8)(16-13)(16-11)}$

$\implies \sqrt{16*8*3*5}$

$\implies \sqrt{8*8*2*3*5}$

$\implies 8\sqrt{30}$

The area of the triangle is : $8\sqrt{30}$cm²

Hope it helps.