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High School Math : How to find the perimeter of a right triangle

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Example Questions

Example Question #82 : Right Triangles

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

Possible Answers:

$\displaystyle 29$

$\displaystyle 30$

$\displaystyle 32$

$\displaystyle 31$

Correct answer:

$\displaystyle 30$

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 $\displaystyle 5+12+13$

Add the numbers together to get the answer $\displaystyle 30$.

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Example Question #11 : Triangles

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

The points are $\displaystyle (-1,5) (-1,1) (4,5)$.

What is the perimeter of the triangle?

Possible Answers:

$9 + \sqrt{26}$ $\displaystyle 9 + \sqrt{26}$

$\displaystyle 9$

$9 + \sqrt{41}$ $\displaystyle 9 + \sqrt{41}$

$9 + \sqrt{71}$ $\displaystyle 9 + \sqrt{71}$

Correct answer:

$9 + \sqrt{41}$ $\displaystyle 9 + \sqrt{41}$

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 $\sqrt{41}$ $\displaystyle \sqrt{41}$.

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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:

$6+6\sqrt{3}m$ $\displaystyle 6+6\sqrt{3}m$

$6+2\sqrt{3}m$ $\displaystyle 6+2\sqrt{3}m$

$6\sqrt{3}m$ $\displaystyle 6\sqrt{3}m$

$2\sqrt{3}m$ $\displaystyle 2\sqrt{3}m$

$2+2\sqrt{3}m$ $\displaystyle 2+2\sqrt{3}m$

Correct answer:

$6+2\sqrt{3}m$ $\displaystyle 6+2\sqrt{3}m$

Explanation:

The formula for the perimeter of a right triangle is:

$\displaystyle P = s_1 + s_2 + s_3$

where $\displaystyle s$ is the length of a side.

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

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

Plugging in our values, we get:

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

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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:

$16\sqrt{2}+8m$ $\displaystyle 16\sqrt{2}+8m$

$8\sqrt{2}m$ $\displaystyle 8\sqrt{2}m$

$8\sqrt{2}+8m$ $\displaystyle 8\sqrt{2}+8m$

$16\sqrt{2}m$ $\displaystyle 16\sqrt{2}m$

16m $\displaystyle 16m$

Correct answer:

$8\sqrt{2}+8m$ $\displaystyle 8\sqrt{2}+8m$

Explanation:

The formula for the perimeter of a right triangle is:

$\displaystyle P = s_1 + s_2 + s_3$

where $\displaystyle s$ is the length of a side.

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

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

Plugging in our values, we get:

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

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Example Question #1 : How To Find The Perimeter Of A Right Triangle

Triangle

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

Possible Answers:

$35+17.5\sqrt{2}$ $\displaystyle 35+17.5\sqrt{2}$

$52.5\sqrt{3}$ $\displaystyle 52.5\sqrt{3}$

$17.5+17.5\sqrt{3}$ $\displaystyle 17.5+17.5\sqrt{3}$

$52.5+17.5\sqrt{3}$ $\displaystyle 52.5+17.5\sqrt{3}$

$306.25\sqrt{3}$ $\displaystyle 306.25\sqrt{3}$

Correct answer:

$52.5+17.5\sqrt{3}$ $\displaystyle 52.5+17.5\sqrt{3}$

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:

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

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High School Math : How to find the perimeter of a right triangle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #82 : Right Triangles

Example Question #11 : 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 #1 : How To Find The Perimeter Of A Right Triangle

All High School Math Resources

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