Question

if every side of triangle is doubled then the find the percentage increase in the area of triangle​

Answer 1

Answer:

Given:

Each side is doubled

To Find:

Percentage change in the area.

Concept Used:

If sides of a triangle are a, b, and c, then area of a triangle is given by:

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

Where s is the semiperimeter of the triangle.

⇒ $s=\frac{a+b+c}{2}$

Assumption:

Let the sides of the triangle be a, b, and c

Explanation:-

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

As the sides are doubled, new sides are 2a, 2b, and 2c.

⇒ $s=\frac{2a+2b+2c}{2}$

⇒ $s=a+b+c$

⇒ $s=2s$

⇒ New Area = $\sqrt{s(s-2a)(s-2b)(s-2c)}$

⇒ New Area = $\sqrt{2s(2s-2a)(2s-2b)(2s-2c)}$

⇒ New Area = √ 2 × 2 × 2 × 2 × s(s-a)(s-b)(s-c)

⇒ New Area = $4\sqrt{s(s-a)(s-b)(s-c)}$

New Area = 4 times Original Area

Change in Area = New Area – Original Area

Change in Area = 3 times Original Area

⇒ Percentage change in Area = $\frac{Change \: in \: Area}{Original \: Area} X \: 10$

⇒ Percentage change in Area = $\frac{3 \: X \: Original \: Area }{Original \: Area} \: X \: 100$

⇒ Percentage change in Area = 300%

Hence, the percentage change in area is 300%.

Answer 2

Answer:

300% is the correct answer