Question

A triangle is enlarged by a factor of 3. The perimeter of the new triangle is 36 feet. What could be the lengths of the sides of the original triangle?

Answer 1

A. 3 feet, 4 feet, and 5 feet

Answer 2

The possible sides of the triangle may be 3, 4, 5 feet.

Explanation:

Let the sides of a triangle are x, y, z. If these sides are enlarged by a factor of 3 then these sides will become 3x, 3y, and 3z.

Now the perimeter of the given triangle will be

P = 3(x + y + z) = 36

So x + y + z = 12

since to form a triangle condition that should be followed is

x + y > z

Therefore by hit and trial method sides of the triangle may be 3, 4, and 5 which we can check by putting the values of the sides in the original equation.

x + y > z ⇒ 3 + 4 > 5 ⇒ 7 > 5

and 3( x + y + z) = 3(3 + 4 + 5) = 3×12 = 36