Question

In an isosceles triangle, the two congruent legs are doubled in length while the base remains the same. How much longer is the perimeter of the new triangle?

Twice as long
Three times as long
Four times as long
Cannot be determined

Answer 1

If you knew something about the base, like for example, say the base was half the length of the side legs, you might be able to set up an equation to determine how much perimeter increases...

As it is though, with no more information, you have:
Perimeter 1 = b + 2L
Perimeter 2 = b + 4L

Do you see any way to know whether perimeter 2 is twice, three times, or four times as long as perimeter 1?

Answer 2

2 times

Answer 3

?

Answer 4

I didn't see any way to determine it.

Answer 5

4L is twice 2L, but you still don't know anything about the base.

Answer 6

For an example, with numbers, imagine if the side lengths were 4 at first, but the base is unknown.

So you have 4 + 4 + B = 8 + B

then you double the sides, and you get 8 + 8 + B = 16 + B

But I don't see how you would know how much bigger 16 + B is than 8 +B

Answer 7

oh i gotcha

Answer 8

If they said something like "base = half of leg"
you could set up: Perimeter 1 = L + L + 1/2 L
and Perimeter 2 = 2L + 2L + 1/2 L

Then you could determine the ratio.

Since they didn't tell you anything about the base, though, you don't know enough to solve the ratio.