Question

12. If AB= 13 inches and AC = 4 inches, what is the

perimeter of triangle ABC?
F. 17 inches
G. 21 inches
H. 26 inches
J. 30 inches

Answer 1

The correct answer is J. The perimeter of triangle ABC is approximately 30 inches. To find the perimeter of triangle ABC, we need to calculate the lengths of all three sides. Given AB = 13 inches and AC = 4 inches, we can use the Pythagorean theorem to find BC. After finding BC, we add the lengths of all three sides together to get the perimeter. In this case, the perimeter is approximately 30 inches.

To find the perimeter of triangle ABC, we need to add the lengths of all three sides together.

Given:

AB = 13 inches

AC = 4 inches

To find the missing side, BC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's denote BC as x.

Using the Pythagorean theorem:

`AB^2 = AC^2 + BC^2`

`13^2 = 4^2 + x^2`

169 = 16 +
`x^2`

`x^2` = 169 - 16

`x^2` = 153

x = √153 (approx. 12.37 inches)

Now, we can calculate the perimeter by adding the lengths of all three sides:

Perimeter = AB + AC + BC

Perimeter = 13 + 4 + √153

Perimeter ≈ 17 + 12.37

Perimeter ≈ 29.37 inches

The closest option to 29.37 inches among the given choices is 30 inches (J).

Therefore, the correct answer is J. The perimeter of triangle ABC is approximately 30 inches.