Question

the perimeter of triangle is 50 cm.one side of triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. find the areas of triangle.​

Answer 1

Answer:

Let the smallest side of the triangle be x cm long

So, second side =(x+4)cm

and third side =(2x−6)cm

Given, perimeter =50cm

Therefore, x+(x+4)+(2x−6)=50

⇒4x=52

⇒x=13cm

So, first side of the triangle is 13cm, second side be 17cm and third side is 20cm.

Now, semi-perimeter of the triangle

$\frac{13 + 17 + 20}{2}$

=25cm

Therefore, area of Δ=

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

$= \sqrt{25(25 - 12)(25 - 17)(25 - 20)}$

$= \sqrt{25 \times 12 \times 8 \times 5}$

$= 20 \sqrt{30} cm {}^{2}$