Question

if each side of triangle is double then find the ratio of area of a new triangle thus form and given triangle ​

Answer 1

Answer:

i hope it will help you...

Step-by-step explanation:

let one side of a triangle be x

then the corresponding side of this new triangle is 2x because it is doubled

sides of new triangle and given triangle are in proportion

∴given triangle is similar to new triangle

new triangle and the given triangle are similar triangles.

by using area of similar triangles theorem,

area of new triangle/area of given triangle=(2x/x)²

                                                                 =4x²/x²  

                                                                =4:1                                                          

∴ratio of area of new triangle and the given triangle=4:1

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Answer 2

$\huge\mathfrak\red {answer:-}$

_________________________________________$<b>$

Let the sides of Triangle a,b,c

==> Semiperimeter of Triangle (s)

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

==>Area Of Triangle :-

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

Sides Of New Triangle ==> 2a ,2b ,2c.

✴Semiperimeter of Triangle =

$\frac{2a + 2b + 2c}{2}$

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

Area Of New =>

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

$\sqrt{2s \times 2(s - a)2(s - b)2(s - c)}$

$\sqrt{16s(s - a)(s - b)(s - c)}$

$4 \sqrt{s(s - a)(s - b)(s - c)}$

= 4 × Area Of Triangle

$\frac{area \: of \: new \: triangle}{area \: of \: triangle \: } = 4$

$<b>$Hence, the area of the new triangle becomes 4 times the area of the original triangle.

So Ration => 4:1

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$\huge\boxed{Thanks !}$