Perimeter of a Triangle

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Pre-Algebra › Perimeter of a Triangle

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Find the perimeter of the triangle above.

Note: Figure not drawn to scale.

CORRECT

None of these answers are correct.

Explanation

The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: .

Because the lengths are in inches, the answer must be in inches as well.

What is the perimeter of an equilateral triangle with a length of 5?

CORRECT

$\frac{15}{2}$

$\frac{3}{2}$

$\textup{There is not enough information.}$

Explanation

There are three equal sides in an equilateral triangle.

Substitute the side length.

$P=3\times 5 =15$

What is the perimeter of an equillateral triangle with side of length 5.5cm?

$16.5\text{cm}$

CORRECT

$16.5\text{cm}^2$

$27.5\text{cm}$

$27.5\text{cm}^2$

$30.25\text{cm}$

Explanation

The formula to find the perimeter of a triangle is

where a, b, and c are the sides of the triangle. We know that one side of the triangle is 5.5cm. We also know that an equillateral triangle has 3 equal sides. Therefore, all sides are 5.5cm. Using that information, we can substitute into the formula. We get

$P = 5.5\text{cm} +5.5\text{cm} +5.5\text{cm}$

$P = 16.5\text{cm}$

Note that we do not combine the labels, only the coefficients.

If the area of an equilateral triangle is 10, and the height is 10, what must be the perimeter of the triangle?

CORRECT

$\textup{There is not enough information.}$

Explanation

Write area formula for a triangle.

$A=\frac{1}{2} bh$

Substitute the area and the height to find the length of the base.

$10=\frac{1}{2} b(10)$

The base, or the length one side of the triangle, is two.

An equilateral triangle has three equal sides. Multiply the base by three to find the perimeter.

The answer is:

An equilateral triangle measures inches along its three equal sides. What is the area of the triangle?

inches

CORRECT

inches

Explanation

To find the perimeter of any object, simply add the length of each side together. The best answer is:

inches

What is the perimeter of an isosceles triangle with a base length of ?

$\textup{There is not enough information.}$

CORRECT

Explanation

For an isosceles triangle, two of the side legs are equal. It is necessary to know two of the three sides in order to sum the lengths. The problem only gave us the length of the base.

There is not enough information to solve this question since the length of the other leg is unknown.

What is the perimeter of a right triangle with hypotenuse and a leg of length ?

CORRECT

It cannot be determined from the information given.

Explanation

Using the Pythagorean Theorem, the length of the second leg can be determined.

We are given the length of the hypotenuse and one leg.

$b^2=c^2-a^2\rightarrow b=\sqrt{c^2-a^2}$

$\sqrt{91^{2}-35^{2}} = \sqrt{8,281-1,225} = \sqrt{7,056} = 84$

The perimeter of the triangle is the sum of the lengths of the sides.

A right triangle has two short sides with lengths 5 and 12. What is the perimeter of the triangle?

CORRECT

Explanation

To begin, first find the length of the third side of the triangle. We are given that the two short sides of the triangle have lengths of 5 and 12. Use the Pythagorean Theorem to find the length of the third side:

$\small a^2+b^2=c^2$ ,