Question

1. what is the perimeter of triangle abc, to the nearest tenth? a 7 in c b 4 in

Explanation:

Step1: Identify triangle type

Triangle \( ABC \) is right - angled at \( C \), so we can use the Pythagorean theorem \( AB^{2}=AC^{2}+BC^{2} \) to find the length of \( AB \). Given \( AC = 7 \) in and \( BC = 4 \) in.

Step2: Calculate length of \( AB \)

Substitute \( AC = 7 \) and \( BC = 4 \) into the Pythagorean theorem:
\( AB=\sqrt{AC^{2}+BC^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{49 + 16}=\sqrt{65}\approx8.1 \) (rounded to the nearest tenth)

Step3: Calculate the perimeter

The perimeter \( P \) of a triangle is the sum of its three sides. So \( P=AC + BC+AB \).
Substitute \( AC = 7 \), \( BC = 4 \), and \( AB\approx8.1 \) into the formula:
\( P = 7+4 + 8.1=19.1 \)

Answer:

The perimeter of triangle \( ABC \) is \( 19.1 \) inches.