What is the value of x? show your work.

The small arcs inside the triangle show that they are similar, so first find the ratio between the similar sides that both have given lengths.

JK is 25, and MN is 30.

30/25 = 1.2

This means the larger triangle is 1.2 times the size of the smaller one.

So MP needs to equal 1.2 x the length of JL:

JL = 20

20 * 1.2 = 24

Now you have 4x-4 = 24

Now silve for x:

Add 4 to each side:

4x = 28

Divide both sides by 4:

x = 28 / 4

x = 7

So basically the side length went from 3 to 7.5, so we have to find the factor which caused the increase. We have to find what times 3 makes 7.5

So our equation is 3×x=7.5
From here on it's just algebra, we'll divide each side by 3 to isolate x

7.5/3=2.5
x=2.5
So the scale factor applied to the first rectangle is 2.5