Question

if each side of a triangle is doubled then how many times the area of triangle increased

Answer 1

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Answer 2

Answer:

The area of the triangle is increased 4 times.

Step-by-step explanation:

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

Now, area of the triangle is given by the formula :

$Area=\frac{1}{2}\times Base\times Height\\\\\implies \text{Area of smaller triangle = }\frac{1}{2}\times b\times h$

Now, the sides of the triangle are doubled, so new sides of the triangle are : 2a, 2b and 2c

Since, the sides of both the triangles are in proportion. So both the triangles are similar.

⇒ tanθ = tanФ

$\implies \frac{h}{\frac{b}{2}}=\frac{h'}{b}\\\\\implies h'=2\cdot h$

$\text{Area of larger triangle = }\frac{1}{2}\times 2b\times h'\\\\\implies \text{Area of larger triangle = }\frac{1}{2}\times 2b\times 2h\\\\\implies \text{Area of larger triangle = }4\times (\frac{1}{2}\times b\times h)\\\\\implies \text{Area of larger triangle = }4\times \text{Area of smaller triangle}$

Hence, the area of the triangle is increased 4 times.