Question

The perimeter of a triangle is 50cm. One side of a triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side. Find the area of the triangle.

• A. $5\sqrt{30}c{m}^2$
• B. $10\sqrt{30}c{m}^2$
• C. $20\sqrt{30}c{m}^2$
• D. $15\sqrt{30}c{m}^2$

Answer 1

The correct option is C

$20\sqrt{30}c{m}^2$

Let the smaller side of the triangle be $xcm$. Therefore, the second side will be $(x+4)cm$, and third side is $(2x-6)cm$.

Now perimeter of triangle

$=x+(x+4)+(2x-6)$

$=(4x-2)cm$

Also perimeter of triangle $=50cm$.

$4x=52;x=\frac{52}{4}=13$

Therefore, the three sides are 13cm, 17cm, 20cm

$s=\frac{13+17+20}{2}=\frac{50}{2}=25cm$

$\therefore \text{Area of}\Delta =\sqrt{25(25-13)(25-17)(25-20)}$

$=\sqrt{25\times 12\times 8\times 5}=\sqrt{5\times 5\times 4\times 3\times 4\times 2\times 5}$

$=5\times 4\times \sqrt{3\times 2\times 5}=20\sqrt{30}c{m}^2$