Question

1. the ratio of the sides of a triangle is 2:6:7. if the perimeter of the triangle is 195 meters, what is the length of the longest side?

2.13
2.13
6.13
7.13
2x + 6x + 7x = 195
m∠1 = 26°
m∠2 = 78°
m∠3 = 91°
15x = 195
15 15
x = 13
91°

1. what is the scale factor of figure b to figure a?
2. if △ghj ~ △lmk, with a scale factor of 5:6, find the perimeter of △ghj.

Explanation:

Step1: Calculate the perimeter of $\triangle LMK$

The perimeter of a triangle is the sum of its side lengths.
For $\triangle LMK$, the side lengths are \(14\), \(11\), and \(17\).

$$P_{LMK}=14 + 11+17=42$$

Step2: Use the scale - factor to find the perimeter of $\triangle GHJ$

Given the scale factor of \(\triangle GHJ:\triangle LMK = 5:6\). Let \(P_{GHJ}\) be the perimeter of \(\triangle GHJ\).
We know that \(\frac{P_{GHJ}}{P_{LMK}}=\frac{5}{6}\)
Substitute \(P_{LMK} = 42\) into the equation:

$$P_{GHJ}=\frac{5}{6}\times P_{LMK}$$

$$P_{GHJ}=\frac{5}{6}\times42$$

$$P_{GHJ}=5\times7 = 35$$

Answer:

The perimeter of \(\triangle GHJ\) is \(35\)