Question

if each side of a scalene triangle is doubled then area would be increased by​

Answer 1

Step-by-step explanation:

as we get area by Heron's formula,

let the 3 sides be a,b and c

so,

S= a+b+c/2

BUT

now you have each side doubled so,

S= (2a+2b+2c)/2

S= a+b+c

so, S has doubled.

so area = √{2S (2S-2a)(2S-2b)(2s-2c)}

=> √4{ S(S-a)(S-b)(S-c)}

=> 2 × area

Therefore, area doubles!

Hope it helped.

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Answer 2

The area of the triangle increases 4 times if each side of a scalene triangle is doubled.

Step-by-step explanation:

We are given the following in the question:

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

Then, the half perimeter is

$s=\displaystyle\frac{a+b+c}{2}$

Area of triangle by Heron's Formula is:

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

If the side of the scalene triangle are doubled, then,

New half perimeter is

$s'=\displaystyle\frac{2a+2b+2c}{2} = 2s$

Area of new triangle =

$A' = \sqrt{s'(s'-2a)(s'-2b)(s'-2c)}\\A' = \sqrt{2s(2s-2a)(2s-2b)(2s-2c)}\\A' = \sqrt{16s(s-a)(s-b)(s-c)}\\A' = 4\sqrt{s(s-a)(s-b)(s-c)}\\A' = 4A$

Thus, the area of the triangle increases 4 times if each side of a scalene triangle is doubled.

#LearnMore

What is the area of the triangle if it's sides are 35cm,84cm,91cm . (SCALEN TRIANGLE).

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