Question

I need HELP please


Thank you

Answer 1

Length NJ = x = 3

Explanation:

Since the pentagons are similar, the ratio of each side of pentagon ABCDE to the corresponding side of pentagon JKLMN must be the same for all sides

Therefore

`(AB)/(JK) = (BC)/(KL) =(CD)/(LM) = (DE)/(MN) = (EA)/(NJ)`

From the values provided for the lengths of the sides of the two pentagons this works out to:

`(2)/(1) = (3)/(1.5) = (3)/(1.5) = (2)/(1) = (6)/(x)`

Each of the computable ratios = 2

This means
each side of pentagon ABCDE = 2 x each side of pentagon JKLMN

Therefore we get
EA = 2 · NJ

6 = 2 x

x2x = 6

x = 6/2

x = 3

Note
I did not have to calculate all ratios. If the pentagons are similar, the ratios of the sides must be the same and therefore I needed to calculate only one ratio.

I wanted to cover all bases and make sure you understood