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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #511 : Plane Geometry

A checkerboard has an area of $315\;cm^2$ and one of the sides has a length of $15\;cm$ . What is the length of the other side of the board?

Possible Answers:

$20\;cm$

$19\;cm$

$22\;cm$

$21\;cm$

$18\;cm$

Correct answer:

$21\;cm$

Explanation:

We can use the formula for the area of a rectangle to find the length of the side with the information provided:

$\\Area=length\cdot width\\315\;cm^2=length\cdot15\;cm\\length=\frac{315\;cm^2}{15\;cm}=21\;cm\\length=21\;cm$

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Example Question #511 : Basic Geometry

If a graham cracker has a width of $5\;cm$ and an area of $62.5\;cm^2$ , what would be the length of the cracker?

Possible Answers:

$13\;cm$

$12.5\;cm$

$14\;cm$

$12\;cm$

$13.5\;cm$

Correct answer:

$12.5\;cm$

Explanation:

We can solve for the missing length using the formula for area of a rectangle:

$\\area=length\cdot width\\62.5\;cm^2=length\cdot5\;cm$

$length=\frac{62.5\;cm^2}{5\;cm}=12.5\;cm$

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Example Question #511 : Basic Geometry

A rectangle has a width of 5 meters. Its length is 2.5 times the width. What is the length of the long side and the total area of this rectangle?

Possible Answers:

A=50m

L=10m

None of these.

A=80

L=15

A=75m

L=15m

A=62.5m

L=12.5m

Correct answer:

A=62.5m

L=12.5m

Explanation:

"2.5 times the width" is equivalent to 2.5w. The length of the long side is L=2.5w=2.5(5)=12.5m .

The area is A=L*W=12.5*5=62.5m^2

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Example Question #512 : Basic Geometry

A rectangle has a perimeter of 30in . Its width is 5 in. What is the length of one long side?

Possible Answers:

L=20in

L=25in

L=5in

L=10in

None of these.

Correct answer:

L=10in

Explanation:

The perimeter of a rectangle can be found with P=2w+2l .

Fill in the information given, and solve for l:

30=2(5)+2l

30=10+2l

20=2l

$\mathbf{l=10}$

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Example Question #102 : Rectangles

Brady wants create a garage with an area of 2000 square feet. He needs the garage to be 50 feet long to fit all of his equipment. How wide will the garage be?

Possible Answers:

$45\ ft$

$50\ ft$

None of the answers given are correct

$40\ ft$

$30\ ft$

Correct answer:

$40\ ft$

Explanation:

Since we have the area, and we have the length, we use the area of a rectangle formula to find the missing side length.

$length\cdot width = area$

$50\cdot width = 2000$

divide both sides by 50 to get the variable by itself

width=40 inches

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle has a length of 12 in and a width of 5 in. What is the diagonal of the rectangle?

Possible Answers:

$13\; in$

$15\; in$

$14\; in$

$16\; in$

$17\; in$

Correct answer:

$13\; in$

Explanation:

To find the diagonal we use the Pythagorean Theorem:

$5^{2}+12^{2}= x^{2}$ where = hypotenuse

$25+144=x^{2}$ or $x=13\; in$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

One side of a rectangle is 7 inches and another is 9 inches. How many inches long is the rectangle's diagonal?

Possible Answers:

11.4

130

10.2

Correct answer:

11.4

Explanation:

You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

$\sqrt{9^{2}+7^{2}}=11.4$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal.

Possible Answers:

$16\sqrt{13}$

$4\sqrt{13}$

Correct answer:

$4\sqrt{13}$

Explanation:

The rectangle can be cut into two equal right triangles, where the hypotenuse of both is the rectangle's diagonal.

Use the Pythagorean Theorem to find the hypotenuse:

a^2+b^2=c^2 , where a and b are the legs and c is the hypotenuse

(12)^2 + (8)^2 = c^2

144 + 64 = c^2

208 = c^2

$\sqrt{208} = \sqrt{c^2}$

$c = 4\sqrt{13}$

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Example Question #3 : How To Find The Length Of The Diagonal Of A Rectangle

A standard high school basketball court is 84 feet long and 50 feet wide. During practice, Coach K has Kyrie run from one the right corner on one end of the court to the left corner at the other end of the court. To the nearest foot, how far did Kyrie run?

Possible Answers:

87ft

134ft

104ft

93ft

98ft

Correct answer:

98ft

Explanation:

A picture helps greatly with this problem, so we begin with a rectangular basketball court.

We note that the distance run by Kyrie (drawn in red) is the diagonal of our rectangle, which we will call . We should also not that this diagonal divides our rectangle into two congruent right triangles. We can therefore find the length of our diagonal by focusing on one of these triangles and determining the hypotenuse. This can be done with the Pythagorean Theorem, which gives us:

50^2+84^2=k^2

2500+7056=k^2

9556=k^2

Taking the square root gives us

k=97.754795...

Rounding to the nearest foot gives an answer of 98.

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle has a height of and a base of . What is the length of its diagonal rounded to the nearest tenth?

Possible Answers:

30.5

19.5

28.4

12.2

24.4

Correct answer:

24.4

Explanation:

1. Use Pythagorean Theorem with a=14 and b=20 .

$a^{2}+b^{2}=c^{2}$

$14^{2}+20^{2}=c^{2}$

2. Solve for , the length of the diagonal:

$14^{2}+20^{2}=c^{2}$

$196+400=c^{2}$

$596=c^{2}$

c=24.41

This rounds down to 24.4 because the hundredth's place () is less than .

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #511 : Plane Geometry

Example Question #511 : Basic Geometry

Example Question #511 : Basic Geometry

Example Question #512 : Basic Geometry

Example Question #102 : Rectangles

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #3 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

All Basic Geometry Resources

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