Question

If triangle ghj is congruent to triangle lmk, with a scale factor of 5:6, find the perimeter of triangle ghj

Answer 1

Answer:  35

Step-by-step explanation:

1. By definition, the perimeter of a triangle is the sum of the lenght of each side.

2. Then, the perimeter of the triangle LMK is:

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

3. If both triangles are congruent and the scale factor is 5:6 (Which you can rewrite as a fraction: 5/6), you must multiply the perimeter of the triangle   LMK by this scale factor.

4. Then, you have that the perimeter of the triangle GHJ is:

$P_{GHJ}=42*\frac{5}{6}=35$

Answer 2

Triangle GHJ is similar to triangle LMK. The perimeter of the triangle GHJ is 35.5067 units.

Given:

Two triangles GHJ and LMK are similar with a scale factor of 5:6.

The length of sides KL, LM, and MK is 14, 11, and 17, respectively.

Now, the triangles are similar. So, the sides of the triangles will also be in the same ratio. It can be represented as,

$\dfrac{LM}{GH}=\dfrac{MK}{HJ}=\dfrac{KL}{JG}=\dfrac{6}{5}$

So, the sides of triangle GHJ will be,

$\dfrac{LM}{GH}=\dfrac{6}{5}\\\dfrac{11}{GH}=\dfrac{6}{5}\\GH=9.17\\\dfrac{MK}{HJ}=\dfrac{6}{5}\\\dfrac{17}{HJ}=\dfrac{6}{5}\\HJ=14.17\\\dfrac{KL}{JG}=\dfrac{6}{5}\\\dfrac{14}{JG}=\dfrac{6}{5}\\JG=11.67$

So, the perimeter of the triangle GHJ can be calculated as,

$p=GH+HJ+GJ\\p=9.17+14.17+11.67\\p=35.5067$

Therefore, the perimeter of the triangle GHJ is 35.5067 units.

For more details, refer to the link:

https://brainly.com/question/12532161