Question

If the sides of atriangle are doubled, it's area would remain same or changes if changes than it becomes how many times....

Answer 1

Let △ABC△ABC be any triangle.

Let △△DEF be a triangle with each side twice the size of the corresponding side of △ABC.△ABC.

Then, △ABC△ABC and △DEF△DEF are similar triangles.

⇒⇒ If s1s1 are s2s2 are the corresponding sides of △ABC△ABC and △DEF,△DEF, s2=2s1.s2=2s1.

Let A1A1 and A2A2 be the areas of △ABC△ABC and △DEF△DEF respectively.

Then, by the property of similar triangles, A2A1=(s2s1)2.A2A1=(s2s1)2.

⇒⇒ A2A1=(2s1s1)2=4.A2A1=(2s1s1)2=4.

⇒⇒ The area of the new triangle would be four times that of the old triangle.

⇒⇒ The area would be increased three times.

Answer 2

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