Question

The perimeter of kite LMNO is 80 feet. Side MN = 3x + 5 and side NO = x – 7. What is the length of MN?

Answer 1

Is there a figure?

Answer 2

answers given:
36.5
31.5
3.5
32

Answer 3

and sure let me draw it one sec

Answer 4

The perimeter is the sum of the lengths of all 4 sides.
Set up an equation where you add all side lengths and set it equal to 80.
Then solve for x.

Answer 5

i tried doing that but i couldnt come up with a number

Answer 6

Let's try it together.
Two sides have given lengths.
I'll write the lengths in the figure you drew.

Answer 7

Can you write the lengths of sides LM and LO in the figure?

Answer 8

its the same thing right?

Answer 9

Correct.

Answer 10

Now we add all side lengths up and set the sum equal to 80.

3x + 5 + 3x + 5 + x - 7 + x - 7 = 80

Ok so far?

Answer 11

yeah

Answer 12

3x + 5 + 3x + 5 + x - 7 + x - 7 = 80

Combine like terms on the left side.

3x + 3x + x + x + 5 + 5 - 7 - 7 = 80

8x - 4 = 80

Ok?

Answer 13

ok

Answer 14

so x would be 10.5 right?

Answer 15

Add 4 to both sides:

8x = 84

Divide both sides by 8:

x = 10.5

Answer 16

Yes.
Now we can check to see if we are correct.

Answer 17

10.5- 7 = 3.5

Answer 18

The sides measuring 3x + 5 really measure 3(10.5) + 5 = 36.5
The sides measuring x - 7 really measure 10.5 - 7 = 3.5

Ok?

Answer 19

ok :)

Answer 20

The perimeter is the sum of all 4 lengths:
36.5 + 36.5 + 3.5 + 3.5 = 80
That means our value of x is correct.

Answer 21

yay ! perfect

Answer 22

MN = 3x + 5 = 3(10.5) + 5 = 36.5

Answer 23

Great.