ISEE Upper Level Quantitative Reasoning - How to find the perimeter of a square

Find the perimeter of a square with a width of 4cm.

$16\text{cm}$

$8\text{cm}$

$12\text{cm}$

$24\text{cm}$

$\text{There is not enough information to solve the problem.}$

Explanation

To find the perimeter of a square, we will use the following formula:

$\text{perimeter of square} = a+b+c+d$

where a, b, c, and d are the lengths of the sides of the square.

Now, we know the width of the square has a length of 4cm. Because it is a square, all sides are equal. Therefore, all sides are 4cm.

Knowing this, we can substitute into the formula. We get

$\text{perimeter of square} = 4\text{cm} +4\text{cm} +4\text{cm} +4\text{cm}$

$\text{perimeter of square} = 16\text{cm}$

Find the perimeter of a square with a width of 18in.

$72\text{in}$

$36\text{in}$

$96\text{in}$

$64\text{in}$

$\text{There is not enough information to solve the problem.}$

Explanation

To find the perimeter of a square, we will use the following formula:

where a, b, c, and d are the lengths of the sides of the square.

Now, we know the width of the square is 18in. Because it is a square, all sides are equal. Therefore, all sides are 18in.

So, we get

$P = 18\text{in} + 18\text{in} + 18\text{in} + 18\text{in}$

$P = 72\text{in}$

Inscribed circle

In the above diagram, the circle is inscribed inside the square. The circle has circumference 30. What is the perimeter of the square?

$\frac{120}{\pi}$

$120 \pi$

$60 \pi$

$\frac{60}{\pi}$

Explanation

Call the diameter of the circle . The length of each side of the square also is equal to this.

The diameter of the circle is equal to its circumference divided by $\pi$ , so

$d = \frac{C}{ \pi} = \frac{30}{ \pi}$ .

The perimeter of the square is four times this sidelength, so

$P= 4d = 4 \cdot \frac{30 }{\pi} = \frac{120}{\pi}$ .

Find the perimeter of a square with a side length of .

Explanation

A square has 4 equal sides.

Write the formula for the perimeter of a square.

Substitute the side length.

Evaluate the terms on the right.

The answer is:

While out walking, you find a strange, square-shaped piece of metal. If the side length of the piece is 26 inches, what is the perimeter of the square?

Explanation

While out walking, you find a strange, square-shaped piece of metal. If the side length of the piece is 26 inches, what is the perimeter of the square?

To find the perimeter of a square, simply multiply the side length by 4. We can do this because perimeter is the distance around the outside of a shape, and squares have 4 equal sides.

One of your holiday gifts is wrapped in a cube-shaped box.

If one of the edges has a length of 6 inches, what is the perimeter of one side of the box?

Explanation

One of your holiday gifts is wrapped in a cube-shaped box.

If one of the edges has a length of 6 inches, what is the perimeter of one side of the box?

To find perimeter of a square, simply multiply the side length by 4

$Perimeter_{square}=4*6in=24 in$

If the area of a square is $25x^{2}$ , what is the perimeter?

$5x^{2}$

$4x^{2}$

Explanation

If the area of a square is $25x^{2}$ , then the length of one side will be equal to the square root of $25x^{2}$ .

$\sqrt{25x^{2}}=5x$

The perimeter is equal to 4 times the length of one side.

This gives us: $5x\cdot 4 = 20x$

Side shown below in square is equal to 17.5 inches. What is the perimeter of ?

$70\ in$

$35\ in$

$306.25\ in$

$17.5\ in$

Cannot be determined

Explanation

The perimeter of a quadrilateral is the sum of the length of all four sides. In a square, each side is of equal length. Thus, the perimeter is the length of a side (given) times 4.

$17.5\times4=70$

Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the perimeter of her room?

Not enough information to solve the problem

Explanation

Your new friend has a very small, square-shaped dorm room. She tells you that it is only 225 square feet. Assuming this is true, what is the perimeter of her room?

So, we need to find the perimeter of a square. First, we need to find the side length.

Let's begin with our formula for the area of a square: