# GMAT Math : Calculating the length of the side of a square

## Example Questions

### Example Question #1 : Calculating The Length Of The Side Of A Square

Square A has twice the sidelength of Square B. The total area of the squares is 605 square feet. What is the sidelength of Square B?

Explanation:

Let  be the sidelength of Square B. Then the sidelength of Square A is , and the areas of Squares A and B are  and , respectively. Since the areas add up to 605 square feet, we solve for  in this equation:

feet

### Example Question #2 : Calculating The Length Of The Side Of A Square

The perimeter of a square plus its area is equal to . What is the length of a side of the square?

Explanation:

First we must set up the equation described by the first sentence of the problem. It tells us the perimeter of a square plus its area is equal to . We want to write this in terms of length, so we can write the following:

Where  is the length of one side of the square. We then bring over the  to write the equation as a polynomial that we can factor. This gives us:

A negative length makes no sense, so we can cross out the first result and we're left with the answer, .  We could plug this length back into the original formula and see that a square with this side length would have a perimeter of  and an area of , which add up to , verifying the solution.

### Example Question #3 : Calculating The Length Of The Side Of A Square

A circle is inscribed in a square. The area of the circle is . What is the area of the square?

Explanation:

Since we know the area of the circle, we can tell that: . Where  is the radius of the circle.

The length of a side of the square will be  since the diameter of the circle is the same length as the side length of the square.

Finally we can calculate the area of the square which will be  so the area will be , which is our final answer.

### Example Question #4 : Calculating The Length Of The Side Of A Square

A circle is inscribed in a square. The square has an area of , what is the perimeter of the circle?

Explanation:

The square as an area of 3. From that we can figure out the length of a side of the square, which is the same size as the diameter of the circle.

From the diameter of the circle we can find out, the perimeter of the circle given by the formula: , where  is the length of the diamter.

So  and therefore, the final answer is .

### Example Question #5 : Calculating The Length Of The Side Of A Square

is a square, and  is the midpoint of diagonal . What is the length of the side of the square?

Explanation:

Since BE is half of the diagonal BD, it follows that the size of the diagonal must be .

The length of a diagonal of a square will always be , where  is the length of the side of the square.

Since the diagonal is , the side of the square must be 2.

### Example Question #6 : Calculating The Length Of The Side Of A Square

Two squares in the same plane have the same center. The length of one side of the smaller square is 10; the area of the region between the squares is 60. Give the length of one side of the larger square.

Explanation:

Let  be the length of one side of the larger square. Then the larger square has area ; the smaller square has area . The area of the region between them, 60, is their difference:

### Example Question #7 : Calculating The Length Of The Side Of A Square

Two squares in the same plane have the same center. The length of one side of the larger square is 10; the area of the region between the squares is 60. Give the length of one side of the smaller square.