Need help with geometry please!?

Question

The perimeter of parallelogram STOP is 54 cm. Segment ST is 1 cm longer than segment SP. Find ST and SP.

How do you solve this? Thanks!

Answer 1

Draw the parallelogram and name the four points S T O P going clockwise. Above the line of ST and PO write x+1. Next to TO and SP write x.

54= x+1+x+1+x+x
54=4x+2
52=4x
13=x

Then plug it back in.

ST is x+1 so it is 13+1=14cm
SP is x so it is 13cm.

Answer 2

Well, on parallelograms the opposite sides are the same in length and on this one, the segment ST is longer than the segment SP. So, your parallelogram should look like this (with S being the upper left corner and continuing clockwise until P is in the lower left corner):

http://www.auburn.wednet.edu/everydaymath/images/parallelogram.jpg

Now, you know that the length of sides SP and TO is x while the length of sides ST and PO is x + 1cm. Knowing that, we can say that all of the sides of the perimeter add together to get 54 cm. So, you do the following:

ST+PO+SP+TO= 54 cm
so
(x+1)+(x+1)+x+x= 54cm
so
4x+2=54cm
so
4x=52cm
so
x=13cm
this means that
ST= 14cm
PO= 14 cm
SP=13 cm
TO=13 cm


There you go, hope that helps!

Answer 3

ST= x+1
SP= x
2(x+1)+2(x)= 54
2x+2+2x= 54
4x+2=54
4x=54
x= 13
ST= 14cm
SP= 13 cm
=) this is definately correct!!!! =D