GED Math - Perimeter and Sides of Triangles

Use the following triangle to answer the question:

Triangle1

Find the perimeter.

$22\text{in}$

$30\text{in}$

$27\text{in}$

$11\text{in}$

$13\text{in}$

Explanation

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

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

Now, given the triangle

Triangle1

we can see it has lengths of 9in, 3in, and 10in. Knowing this, we can substitute into the formula. We get

$P = 9\text{in} + 3\text{in} + 10\text{in}$

$P = 22\text{in}$

If one side of an isosceles triangle is 8 cm and the base is half the length of the side, what is the perimeter of the triangle?

Explanation

First we need to know that in an isosceles triangle, 2 sides are equal in size so we know that since one side is 8cm, the other side is also 8cm.

We are also given information that the base is half the length of the size, and half of 8 is 4, so our base is 4cm.

The perimeter of any triangle is found when adding up all sides.

In this case we add up

If $\Delta MNO \cong \Delta PQR$ , then which segment is congruent to $\overline{NO}$ ?

$\overline{RQ}$

$\overline{RP}$

$\overline{MO}$

$\overline{NQ}$

Explanation

A congruency statement about two triangles implies nothing about the relationship between two sides of the same triangle, so we can eliminate $\overline{MO}$ . Also, the length of a segment with endpoints on two different triangles depends on their positioning, not their congruence, so we can eliminate $\overline{NQ}$ .

Since and are in the same positions in the name of the first triangle as and , $\overline{NO}$ and $\overline{QR}$ are corresponding sides of congruent triangles, and

$\overline{NO} \cong \overline{QR}$ .

Since the letters of the name of a segment are interchangeable, this statement can be rewritten as

$\overline{NO} \cong \overline{RQ}$ ,

making $\overline{RQ}$ the correct choice.

The perimeter of an equilateral triangle is 36in. Find the length of one side.

$12\text{in}$

$13\text{in}$

$14\text{in}$

$11\text{in}$

$9\text{in}$

Explanation

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. Because it is an equilateral triangle, all sides are equal. Therefore, we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the equilateral triangle is 36in. So, we will substitute and solve for a. We get

$36\text{in} = 3a$

$\frac{36\text{in}}{3} = \frac{3a}{3}$

$12\text{in} = a$

$a = 12\text{in}$

Therefore, the length of one side of the equilateral triangle is 12in.

A triangle has sides of length 14, 19, and 23. Which of the following is a true statement?

The triangle is scalene and acute.

The triangle is scalene and obtuse.

The triangle is isosceles and acute.

The triangle is isosceles and obtuse.

Explanation

No two of the sides are of equal length, making the triangle scalene.

To determine whether it is acute or obtuse, add the squares of the lesser lengths, and compare the sum to the square of the greatest length:

$14^{2}= 14 \times 14 = 196$

$19 ^{2}= 19 \times 19 = 361$

$14^{2} + 19 ^{2} = 196+ 361 = 557$

$23^{2}= 23 \times 23 = 529$

$14^{2} + 19 ^{2} > 23^{2}$

The sum of the squares of the lesser lengths exceeds the square of the greatest length, so the triangle is acute.

The correct response is that the triangle is scalene and acute.

An equilateral triangle has a perimeter of 69in. Find the length of one side.

$23\text{in}$

$36\text{in}$

$33\text{in}$

$32\text{in}$

$18\text{in}$

Explanation

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. Because an equilateral triangle has 3 equal sides, we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the triangle is 69in. So, we can substitute and solve for a. We get

$69\text{in} = 3a$

$\frac{69\text{in}}{3} = \frac{3a}{3}$

$23\text{in} = a$

$a = 23\text{in}$

Therefore, the length of one side of the equilateral triangle is 23in.

An equilateral triangle has a perimeter of 123in. Find the length of one side.

$41\text{in}$

$36\text{in}$

$33\text{in}$

$29\text{in}$

$14\text{in}$

Explanation

The formula to find the perimeter of an equilateral triangle is

where a is the length of one side of the triangle. An equilateral triangle has 3 equal sides, so we can use any side in the formula. To find the length of one side, we will solve for a.

Now, we know the perimeter of the triangle is 123in. So, we will substitute and solve for a. We get

$123\text{in} = 3a$