Question

The turtle shaped sandbox holds 6 cubic feet of sand. The dimensions of the next size turtle sandbox are double the size of the smaller one. How much sand will the larger sandbox hold?

Answer 1

`x*2*6`

Explanation:

When you double the dimensions of the sandbox, you must double all the dimensions. That means that every side is going to have to be multiplied by two in order to find the answer. For example, if you have a rectangle that's `4`m long and `6`m wide and then double the size, you must double both sides.
So, `4*2=8` and `6*2=12` so the dimensions of the next rectangle (assuming that the size is doubled) is `8`m by `6`m.

Thus, the area of the rectangle is `(4*2)*(6*2)=8*12=96`

However, there's a simpler way to solve this question. If we know how many sides the rectangle has, we thus know how many sides we need to double: 2 sides. Knowing this, we can simplify the above equation to `(2*2)*24=96` where the second `2` represents the number of times you're increasing the size of the rectangle by, in this case, `2` times.

Now take the turtle-shaped sandbox. The sandbox has an unknown amount of sides so we don't know how many lengths we need to double and therefore we can't answer the question. We can, however, use `x` to represent the number of sides the sandbox has and plug in a number later on to solve the equation. That would look as follows:

`x*2*6`

By multiplying the number of sides the shape has by `2`, you're doubling the length of all of the sides, giving you the correct answer.