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GED Math : GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Squares, Rectangles, And Parallelograms

Pentagons

Refer to the above diagram. Parallel sides are so indicated.

Identify the above polygon.

Possible Answers:

Parallelogram

Trapezoid

Hexagon

Pentagon

Correct answer:

Trapezoid

Explanation:

A four-sided figure, or quadrilateral, with one pair of parallel sides and its other sides nonparallel is called a trapezoid.

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Example Question #3 : Perimeter And Sides Of Quadrilaterals

Thingy

Refer to the above figure. You are given that $\overleftrightarrow{AE} ||\overleftrightarrow{BD}$ and that $\angle FCD$ is acute.

Which of the following words accurately describes Polygon EFCD ?

Possible Answers:

Pentagon

Hexagon

Parallelogram

Trapezoid

Correct answer:

Trapezoid

Explanation:

Polygon EFCD has four sides and is therefore a quadrilateral. $\overleftrightarrow{AE} ||\overleftrightarrow{BD}$ , so $\overline{FE }|| \overline{CD}$ . Also, since $\angle FCD$ is acute and $\angle CDE$ is right, $\angle FCD \ncong \angle CDE$ , so $\overline{FC } \nparallel \overline{DE}$ .

The quadrilateral has one pair of parallel sides, and the other two sides are not parallel. Therefore, it is a trapezoid.

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Example Question #5 : Squares, Rectangles, And Parallelograms

Pentagons

Refer to the above three figures. All parallel sides are so indicated.

Which of the figures can be called a parallelogram?

Possible Answers:

Figures A, B, and C

Figures A and B only

Figure B only

Figure C only

Correct answer:

Figures A and B only

Explanation:

A parallelogram, by definition, has two pairs of parallel sides. Figures A and B fit that criterion, but Figure C does not.

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Example Question #2 : Squares, Rectangles, And Parallelograms

Garden

Note: Figure NOT drawn to scale.

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in brown). The dirt path is feet wide throughout. Which of the following polynomials gives the perimeter of the garden?

Possible Answers:

320- 4x

320-8x

160-4x

160- 8x

Correct answer:

320-8x

Explanation:

The length of the garden is than that of the entire lot, or

L = 100 - 2x .

The width of the garden is than that of the entire lot, or

W = 60 - 2x .

The perimeter is twice the sum of the two:

P = 2 (L + W)

$= 2 (100-2x+60-2x) = 2\left ( 160-4x\right )= 320-8x$

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Example Question #3 : Squares, Rectangles, And Parallelograms

Rhombus

Note: Figure NOT drawn to scale.

Quadrilateral ABCD is a rhombus. Calculate its perimeter if:

AC = 24

BD = 10

Possible Answers:

Correct answer:

Explanation:

The four sides of a rhombus are congruent. Also, the diagonals of a rhombus are perpendicular bisectors to each other, so the four triangles they form are right triangles. Therefore, the Pythagorean theorem can be used to determine the common sidelength of Quadrilateral ABCD .

We focus on $\Delta AXB$ . The diagonals of a rhombus, as is the case with any parallelogram, are each the other's bisector, so

$AX = \frac{1}{2} (AC) = \frac{1}{2} \cdot 24 = 12$

$XB = \frac{1}{2} (BD) = \frac{1}{2} \cdot 10 = 5$

By the Pythagorean Theorem,

$AB = \sqrt{(AX)^{2}+ (XB)^{2}} = \sqrt{12^{2}+5^{2}} = \sqrt{144+25} = \sqrt{169} = 13$

13 is the common length of the four sides of Quadrilateral ABCD , so its perimeter is $4 \times 13 = 52$ .

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Example Question #5 : Perimeter And Sides Of Quadrilaterals

Rectangle

Note: Figure NOT drawn to scale

AB = 14, BC = 6, AD = 7, DF = 3

Give the ratio of the perimeter of Rectangle ACGF to that of Rectangle ABED .

Possible Answers:

$4\textrm{ to }3$

$100\textrm{ to }49$

$10 \textrm{ to }7$

$1\textrm{ to }1$

Correct answer:

$10 \textrm{ to }7$

Explanation:

The perimeter of Rectangle ABED is

P = AB +BE + ED + AD .

Opposite sides of a rectangle are congruent, so

AB= ED = 14, AD = BE = 7

and

P = 14 + 7 + 14 + 7 = 42 .

The perimeter of Rectangle ACGF is

P = AC + CG + GF + AF .

Opposite sides of a rectangle are congruent, so

GF = AC = AB + BC = 14 + 6 = 20 ,

CG = AF = AD + DF = 7 + 3 = 10 ,

and

P = 20 + 10 + 20 + 10 = 60 .

The ratio of the perimeters is

$\frac{60}{42} = \frac{60\div 6}{42\div 6} =\frac{10}{7}$ - that is, 10 to 7.

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Example Question #11 : Perimeter And Sides Of Quadrilaterals

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in brown). The dirt path is six feet wide throughout. Which of the following polynomials gives the perimeter of the garden, in feet?

Possible Answers:

6x-48

3x-24

6x-24

3x-48

Correct answer:

6x-48

Explanation:

The length of the garden, in feet, is $2 \times 6 = 12$ feet less than that of the entire lot, or

L = 2x-12 .

The width of the garden, in feet, is $2 \times 6 = 12$ less than that of the entire lot, or

W = x-12 .

The perimeter, in feet, is twice the sum of the two:

P = 2 (L + W)

= 2 (2x-12 + x - 12 )= 2 (3x-24) = 6x - 48

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Example Question #1264 : Ged Math

Given Square ABCD , the distance from to is one mile. Which of the following gives the perimeter of the square, to the nearest foot?

Possible Answers:

$29,868\textrm{ ft}$

$10,560\textup{ ft}$

$7,467\textrm{ ft}$

$14,934\textrm{ ft}$

Correct answer:

$14,934\textrm{ ft}$

Explanation:

The segment $\overline{AC}$ is a diagonal of the square. It is also the hypotenuse of a right triangle whose legs both measure the same length, which we will call ; this is also the length of one side of the square.

The right triangle formed is an isosceles triangle - and, subsequently, a $45^{\circ }-45^{\circ }-90^{\circ }$ triangle - and therefore,

$s \sqrt{2} = AC$

$\overline{AC}$ is one mile, or 5,280 feet, long, so we substitute AC = 5,280 and solve for :

$s \sqrt{2} = 5,280$

$s = 5,280 \div \sqrt{2} \approx 5,280 \div 1.414 \approx 3,733.5$

The perimeter, in feet, is four times this, or

$P = 4s \approx 4 \times 3,733.5 \approx 14,934$ feet.

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Example Question #11 : Perimeter And Sides Of Quadrilaterals

The length of each side of a square is increased by 12%. By what percent has its perimeter increased?

Possible Answers:

$48 \%$

$44 \%$

$24 \%$

$12 \%$

Correct answer:

$12 \%$

Explanation:

Let be the original sidelength of the square. Increasing this by 12% is the same as adding 0.12 times that sidelength to the original sidelength. The new sidelength is therefore

s + 0.12s = 1.12s .

The perimeter of a square is four times its sidelength. Its original perimeter was ; after the increase, it is $4 \cdot 1.12s = 4.48 s$ . The percent of increase is therefore

$\frac{4.48s - 4s }{4s} \times 100 \% = \frac{0.48 s}{4s} \times 100 \% = 0.12 \times 100 \% = 12 \%$ .

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Example Question #1261 : Ged Math

The perimeter of a square is 24cm. Find the length of one side of the square.

Possible Answers:

$\text{There is not enough information to answer the question.}$

$3\text{cm}$

$7\text{cm}$

$4\text{cm}$

$6\text{cm}$

Correct answer:

$6\text{cm}$

Explanation:

The formula to find the perimeter of a square is

P = 4a

where a is the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of one side of the square, we will solve for a.

Now, we know the perimeter of the square is 24cm. So, we will substitute and solve for a. We get

$24\text{cm} = 4a$

$\frac{24\text{cm}}{4} = \frac{4a}{4}$

$6\text{cm} = a$

$a = 6\text{cm}$

Therefore, the length of one side of the square is 6cm.

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #2 : Squares, Rectangles, And Parallelograms

Example Question #3 : Perimeter And Sides Of Quadrilaterals

Example Question #5 : Squares, Rectangles, And Parallelograms

Example Question #2 : Squares, Rectangles, And Parallelograms

Example Question #3 : Squares, Rectangles, And Parallelograms

Example Question #5 : Perimeter And Sides Of Quadrilaterals

Example Question #11 : Perimeter And Sides Of Quadrilaterals

Example Question #1264 : Ged Math

Example Question #11 : Perimeter And Sides Of Quadrilaterals

Example Question #1261 : Ged Math

All GED Math Resources

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