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High School Math : High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #91 : Right Triangles

Square PQRS is on the coordinate plane, and each side of the square is parallel to either the -axis or -axis. Point has coordinates $\left ( -2,-1 \right )$ and point has the coordinates $\left ( 3,4 \right )$ .

Quantity A: $5\sqrt{2}$

Quantity B: The distance between points and

Possible Answers:

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information provided.

Quantity A is greater.

Correct answer:

The two quantities are equal.

Explanation:

To find the distance between points and , split the square into two 45-45-90 triangles and find the hypotenuse. The side ratio of the 45-45-90 triangle is $s:s:s\sqrt{2}$ , so if the sides have a length of 5, the hypotenuse must be $5\sqrt{2}$ .

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Example Question #513 : Geometry

Justin travels $15\textup{ feet}$ to the east and $20\textup{ feet}$ to the north. How far away from his starting point is he now?

Possible Answers:

$45\textup{ ft}$

$25\textup{ ft}$

$35\textup{ ft}$

$22\textup{ ft}$

$30\textup{ ft}$

Correct answer:

$25\textup{ ft}$

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that a^2+b^2=c^2

15^2 + 20^2 = c^2

225+400=c^2

625=c^2

25=c

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Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Susie walks north from her house to a park that is 30 meters away. Once she arrives at the park, she turns and walks west for 80 meters to a bench to feed some pigeons. She then walks north for another 30 meters to a concession stand. If Susie returns home in a straight line from the concession stand, how far will she walk from the concession stand to her house, in meters?

Possible Answers:

100

200

Correct answer:

100

Explanation:

Susie walks 30 meters north, then 80 meters west, then 30 meters north again. Thus, she walks 60 meters north and 80 meters west. These two directions are 90 degrees away from one another.

At this point, construct a right triangle with one leg that measures 60 meters and a second leg that is 80 meters.

You can save time by using the 3:4:5 common triangle. 60 and 80 are $3\cdot 20$ and $4\cdot 20$ , respectively, making the hypotenuse equal to $5\cdot 20=100$ .

We can solve for the length of the missing hypotenuse by applying the Pythagorean theorem:

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

Substitute the following known values into the formula and solve for the missing hypotenuse: side .

$a= 60,\ b= 80,\ c= ?$

$(60)^{2}+(80)^{2}=c^{2}$

$3600+6400=c^{2}$

$10,000=c^{2}$

c=100

Susie will walk 100 meters to reach her house.

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Example Question #72 : Triangles

The lengths of the sides of a triangle are consecutive odd numbers and the triangle's perimeter is 57 centimeters. What is the length, in centimeters, of its longest side?

Possible Answers:

Correct answer:

Explanation:

First, define the sides of the triangle. Because the side lengths are consecutive odd numbers, if we define the shortest side will be as , the next side will be defined as x+2 , and the longest side will be defined as x+4 . We can then find the perimeter of a triangle using the following formula:

$\text{Perimeter}=\text{side}+\text{side}+\text{side}$

Substitute in the known values and variables.

$\text{Perimeter}=x+(x+2)+(x+4)$

57=3x+6

Subtract 6 from both sides of the equation.

57-6=3x+6-6

51=3x

Divide both sides of the equation by 3.

$\frac{51}{3}=\frac{3x}{3}$

Solve.

x=17

This is not the answer; we need to find the length of the longest side, or x+4 .

$\text{Longest side}=x+4$

Substitute in the calculated value for and solve.

$\text{Longest side}=17+4$

$\text{Longest side}=21$

The longest side of the triangle is 21 centimeters long.

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Example Question #53 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Each of the following answer choices lists the side lengths of a different triangle. Which of these triangles does not have a right angle?

Possible Answers:

5, 12, 13

$2, 2, 2\sqrt{2}$

6,7,12

9, 12, 15

Correct answer:

6,7,12

Explanation:

6, 7, 12 cannot be the side lengths of a right triangle. 6^2+ 7^2 does not equal 12^2 . Also, special right triangle 3-4-5, 5-12-13, and 45-45-90 rules can eliminate all the other choices.

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Example Question #441 : Geometry

What is the perimeter of a triangle with side lengths of 5, 12, and 13?

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of a triangle you must add all of the side lengths together.

In this case our equation would look like 5+12+13

Add the numbers together to get the answer .

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Example Question #12 : Triangles

Three points in the xy-coordinate system form a triangle.

The points are (-1,5) (-1,1) (4,5) .

What is the perimeter of the triangle?

Possible Answers:

$9 + \sqrt{41}$

$9 + \sqrt{71}$

$9 + \sqrt{26}$

Correct answer:

$9 + \sqrt{41}$

Explanation:

Drawing points gives sides of a right triangle of 4, 5, and an unknown hypotenuse.

Using the pythagorean theorem we find that the hypotenuse is $\sqrt{41}$ .

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Example Question #2 : How To Find The Perimeter Of A Right Triangle

Find the perimeter of the following triangle:

Screen_shot_2014-03-01_at_9.07.42_pm

Possible Answers:

$2+2\sqrt{3}m$

$6\sqrt{3}m$

$2\sqrt{3}m$

$6+6\sqrt{3}m$

$6+2\sqrt{3}m$

Correct answer:

$6+2\sqrt{3}m$

Explanation:

The formula for the perimeter of a right triangle is:

P = s_1 + s_2 + s_3

where is the length of a side.

Use the formulas for a a 30-60-90 triangle to find the length of the base. The formula for a triangle is $a-a \sqrt{3}-2a$ .

Our 30-60-90 triangle is: $2m-2\sqrt{3}m-4m$

Plugging in our values, we get:

$P = 2m+4m+2\sqrt{3}m = 6m+2\sqrt{3}m$

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Example Question #3 : How To Find The Perimeter Of A Right Triangle

Find the perimeter of the following right triangle:

Screen_shot_2014-03-01_at_9.09.16_pm

Possible Answers:

$16\sqrt{2}+8m$

$8\sqrt{2}m$

$8\sqrt{2}+8m$

$16\sqrt{2}m$

16m

Correct answer:

$8\sqrt{2}+8m$

Explanation:

The formula for the perimeter of a right triangle is:

P = s_1 + s_2 + s_3

where is the length of a side.

Use the formulas for a 45-45-90 triangle to find the length of the base and height. The formula for a triangle is $a-a-a \sqrt{2}$

Our 45-45-90 triangle is: $4 \sqrt{2}m-4 \sqrt{2}m-8m$

Plugging in our values, we get:

$P = 4 \sqrt{2}m+4 \sqrt{2}m+8m = 8\sqrt{2}+8m$

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Example Question #443 : Psat Mathematics

Triangle

Based on the information given above, what is the perimeter of triangle ABC?

Possible Answers:

$52.5+17.5\sqrt{3}$

$52.5\sqrt{3}$

$35+17.5\sqrt{2}$

$306.25\sqrt{3}$

$17.5+17.5\sqrt{3}$

Correct answer:

$52.5+17.5\sqrt{3}$

Explanation:

Triangle-solution

Consult the diagram above while reading the solution. Because of what we know about supplementary angles, we can fill in the inner values of the triangle. Angles A and B can be found by the following reductions:

A + 120 = 180; A = 60

B + 150 = 180; B = 30

Since we know A + B + C = 180 and have the values of A and B, we know:

60 + 30 + C = 180; C = 90

This gives us a 30:60:90 triangle. Now, since 17.5 is across from the 30° angle, we know that the other two sides will have to be √3 and 2 times 17.5; therefore, our perimeter will be as follows:

$17.5+2(17.5)+17.5\sqrt{3}=52.2+17.5\sqrt{3}$

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #91 : Right Triangles

Example Question #513 : Geometry

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #72 : Triangles

Example Question #53 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #441 : Geometry

Example Question #12 : Triangles

Example Question #2 : How To Find The Perimeter Of A Right Triangle

Example Question #3 : How To Find The Perimeter Of A Right Triangle

Example Question #443 : Psat Mathematics

All High School Math Resources

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