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High School Math : Squares

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Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Square

The area of square R is 12 times the area of square T. If the area of square R is 48, what is the length of one side of square T?

Possible Answers:

Correct answer:

Explanation:

We start by dividing the area of square R (48) by 12, to come up with the area of square T, 4. Then take the square root of the area to get the length of one side, giving us 2.

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Example Question #31 : Squares

When the side of a certain square is increased by 2 inches, the area of the resulting square is 64 sq. inches greater than the original square. What is the length of the side of the original square, in inches?

Possible Answers:

Correct answer:

Explanation:

Let x represent the length of the original square in inches. Thus the area of the original square is x². Two inches are added to x, which is represented by x+2. The area of the resulting square is (x+2)². We are given that the new square is 64 sq. inches greater than the original. Therefore we can write the algebraic expression:

x² + 64 = (x+2)²

FOIL the right side of the equation.

x² + 64 = x² + 4x + 4

Subtract x²from both sides and then continue with the alegbra.

64 = 4x + 4

64 = 4(x + 1)

16 = x + 1

15 = x

Therefore, the length of the original square is 15 inches.

If you plug in the answer choices, you would need to add 2 inches to the value of the answer choice and then take the difference of two squares. The choice with 15 would be correct because 17² -15² = 64.

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Example Question #261 : Geometry

If the area of a square is 25 inches squared, what is the perimeter?

Possible Answers:

Not enough information

Correct answer:

Explanation:

The area of a square is equal to length times width or length squared (since length and width are equal on a square). Therefore, the length of one side is $l = \sqrt{25in^{2}}$ $\displaystyle l = \sqrt{25in^{2}}$ or $l=5 in.$ $\displaystyle l=5 in.$ The perimeter of a square is the sum of the length of all 4 sides or $4 \times 5 in. =20 in.$ $\displaystyle 4 \times 5 in. =20 in.$

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Example Question #1 : How To Find The Length Of The Side Of A Square

Circleinsquare

A square is inscribed inside a circle, as illustrated above. The radius of the circle is $\frac{3\sqrt{2}}{2}$ $\displaystyle \frac{3\sqrt{2}}{2}$ units. If all of the square's diagonals pass through the circle's center, what is the area of the square?

Possible Answers:

$\displaystyle 3$ units squared

$\frac{9}{2}$ $\displaystyle \frac{9}{2}$ units squared

$\displaystyle 18$ units squared

$\displaystyle 9$ units squared

$\frac{9}{4}$ $\displaystyle \frac{9}{4}$ units squared

Correct answer:

$\displaystyle 9$ units squared

Explanation:

Given that the square's diagonals pass through the circle's center, those diagonals must each form a diameter of the circle. The circle's diameter is twice its radius, i.e. $2 \times \frac{3\sqrt{2}}{2}$ $\displaystyle 2 \times \frac{3\sqrt{2}}{2}$ , which is $3\sqrt{2}$ $\displaystyle 3\sqrt{2}$ . Since this diameter (i.e., the square's diagonal) is the hypotenuse of a right triangle formed by two sides of the square, the length of one of the square's sides can be calculated with the Pythagorean Theorem. $\displaystyle s$ replace $\displaystyle a$ and $\displaystyle b$ because the sides of the square must be equal in length. Since the objective is to solve for the square's area, solve for s^2 $\displaystyle s^2$ since one side squared will be the square's area.

$s^2 + s^2 = (3\sqrt{2})^2$ $\displaystyle s^2 + s^2 = (3\sqrt{2})^2$

$\rightarrow 2s^2 = 18$ $\displaystyle \rightarrow 2s^2 = 18$

$\rightarrow s^2 = 9$ $\displaystyle \rightarrow s^2 = 9$ units squared

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High School Math : Squares

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Length Of The Side Of A Square

Example Question #31 : Squares

Example Question #261 : Geometry

Example Question #1 : How To Find The Length Of The Side Of A Square

All High School Math Resources

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