All GMAT Math Resources
Example Questions
Example Question #7 : Calculating The Perimeter Of A Square
The area of a square is . Give its perimeter.
The length of one side of a square is the square root of the area - or, equivalently, the area raised to the power of . Here, this is
.
Multiply this by 4 to get the perimeter:
Example Question #8 : Calculating The Perimeter Of A Square
A square courtyard will have paths running diagonally across it (the paths will form an x). If the length of one of the paths will be long, what will the perimeter of the courtyard be?
A square courtyard will have paths running diagonally across it (the paths will form an x). If the length of one of the paths will be long, what will the perimeter of the courtyard be?
To find the perimeter of a square, we need to find the side lengths. We can find the side lengths from the diagonal by recalling that the diagonal of a square creates two 45/45/90 triangles.
A 45/45/90 triangle has the following side-length ratios:
This means that if our hypotenuse is long, our other two sides will be 14 meters long
So our side-length is 14 meters, find the perimeter via the following
Example Question #71 : Quadrilaterals
A square is created from joining two equilateral triangles of side length = What is the perimeter of the square?
Draw yourself a picture for this problem. If you create a square out of two triangles, they meet at the diagonal of the square. Since, we know the triangles are equilateral, then all of the side lengths of the triangle and square are equal. Therefore, we just take the side length and add that four times.
Example Question #421 : Problem Solving Questions
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?
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 #421 : Problem Solving Questions
The perimeter of a square plus its area is equal to . What is the length of a side of the square?
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 #181 : Geometry
A circle is inscribed in a square. The area of the circle is . What is the area of the square?
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 #32 : Squares
A circle is inscribed in a square. The square has an area of , what is the perimeter of the circle?
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 #422 : Problem Solving Questions
is a square, and is the midpoint of diagonal . . What is the length of the side of the square?
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 #5 : 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.
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 #1 : 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.
Let be the length of one side of the smaller square. Then the smaller square has area ; the larger square has area . The area of the region between them, 60, is their difference: