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ISEE Lower Level Math : How to find the perimeter of a triangle

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Example Questions

Example Question #91 : Triangles

Find the perimeter of the following triangle:

Triangle6

Possible Answers:

$16\text{ft}$ $\displaystyle 16\text{ft}$

$36\text{ft}$ $\displaystyle 36\text{ft}$

$30\text{ft}$ $\displaystyle 30\text{ft}$

$28\text{ft}$ $\displaystyle 28\text{ft}$

$22\text{ft}$ $\displaystyle 22\text{ft}$

Correct answer:

$28\text{ft}$ $\displaystyle 28\text{ft}$

Explanation:

To find the perimeter of a triangle, we will use the following formula:

$\displaystyle P = a+b+c$

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

Triangle6

we can see it has sides of length 10ft, 6ft, and 12ft. Knowing this, we can substitute into the formula. We get

$P = 10\text{ft} + 6\text{ft} +12\text{ft}$ $\displaystyle P = 10\text{ft} + 6\text{ft} +12\text{ft}$

$P = 28\text{ft}$ $\displaystyle P = 28\text{ft}$

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Example Question #371 : Plane Geometry

Find the length of one side of an equilateral triangle that has a perimeter of 27cm.

Possible Answers:

$9\text{cm}$ $\displaystyle 9\text{cm}$

$5\text{cm}$ $\displaystyle 5\text{cm}$

$6\text{cm}$ $\displaystyle 6\text{cm}$

$7\text{cm}$ $\displaystyle 7\text{cm}$

$8\text{cm}$ $\displaystyle 8\text{cm}$

Correct answer:

$9\text{cm}$ $\displaystyle 9\text{cm}$

Explanation:

The formula to find perimeter of an equilateral triangle is

P = 3a $\displaystyle P = 3a$

where a is the length of one side. We can multiply that by 3, because an equilateral triangle has 3 equal sides. Now, to find the length of one side, we will solve for a.

So, we know the perimeter of the equilateral triangle is 27cm. Knowing this, we can substitute. We get

$27\text{cm} = 3a$ $\displaystyle 27\text{cm} = 3a$

$\frac{27\text{cm}}{3} = \frac{3a}{3}$ $\displaystyle \frac{27\text{cm}}{3} = \frac{3a}{3}$

$9\text{cm} = a$ $\displaystyle 9\text{cm} = a$

$a = 9\text{cm}$ $\displaystyle a = 9\text{cm}$

Therefore, the length of one side of the equilateral triangle is 9cm.

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Example Question #51 : How To Find The Perimeter Of A Triangle

Use the following triangle to answer the question:

Triangle5

Find the perimeter.

Possible Answers:

$19\text{ft}$ $\displaystyle 19\text{ft}$

$17\text{ft}$ $\displaystyle 17\text{ft}$

$18\text{ft}$ $\displaystyle 18\text{ft}$

$20\text{ft}$ $\displaystyle 20\text{ft}$

$16\text{ft}$ $\displaystyle 16\text{ft}$

Correct answer:

$19\text{ft}$ $\displaystyle 19\text{ft}$

Explanation:

To find the perimeter of a triangle, we will use the following formula:

$\displaystyle P = a+b+c$

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

Triangle5

we can see that it has sides of length 8ft, 4ft, and 7ft. So, we get

$P = 8\text{ft} + 4\text{ft} + 7\text{ft}$ $\displaystyle P = 8\text{ft} + 4\text{ft} + 7\text{ft}$

$P = 19\text{ft}$ $\displaystyle P = 19\text{ft}$

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Example Question #51 : How To Find The Perimeter Of A Triangle

An equilateral triangle has a perimeter of 42 cm. What is the length of one of its sides?

Possible Answers:

$14\ cm$ $\displaystyle 14\ cm$

$20\ cm$ $\displaystyle 20\ cm$

$12\ cm$ $\displaystyle 12\ cm$

$10\ cm$ $\displaystyle 10\ cm$

$16\ cm$ $\displaystyle 16\ cm$

Correct answer:

$14\ cm$ $\displaystyle 14\ cm$

Explanation:

By definition, an equilateral triangle is a triangle with three equal sides. That is, the length of each side of the triangle is going to be the same.

In this problem, we know that the perimeter (the sum of all the lengths) is 42 cm.

Side 1 + Side 2 + Side 3 = 42 cm.

Since the sides are equal, we can write the following equation. S = $\displaystyle S =$ one side of the triangle

$\displaystyle 3S=42 cm.$

To find the length of one side of the triangle, we would then divide 3 from both sides.

$\frac{3}{3}S=\frac{42}{3}$ $\displaystyle \frac{3}{3}S=\frac{42}{3}$

1S=14 $\displaystyle 1S=14$ Remember that 1*S $\displaystyle 1*S$ is the same as $\displaystyle S$

$S=14\ cm.$ $\displaystyle S=14\ cm.$

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ISEE Lower Level Math : How to find the perimeter of a triangle

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #91 : Triangles

Example Question #371 : Plane Geometry

Example Question #51 : How To Find The Perimeter Of A Triangle

Example Question #51 : How To Find The Perimeter Of A Triangle

All ISEE Lower Level Math Resources

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