Very, Very hard honors math 5th grade problem?

Question

find the value if x so that the rectangle and the triangle have the same perimeter. What is the perimeter?

sides of rectangle: 2x and 3x-2
sides of triangle: 3x-1, 3x+1, and 3x

I konw that you are supposed to add all the sides of the triangle and the rectangle together. You have to combine like terms.

BUT I DO NOT UNDERSTAND! HELP ME!

Answer 1

Perimeter of rectangle = 2x + 2x + 3x -2 + 3x -2 = 10x - 4

Perimeter of triangle = 3x -1 + 3x + 1 + 3x = 9x

if 9x = 10x - 4

x = 4

Answer 2

sides of rectangle: 2x and 3x-2
sides of triangle: 3x-1, 3x+1, and 3x

The perimeter of the rectangle is
(2)(2x) + (2)(3x-2)=4x + 6x -4 there’s a thing called the distributive property that says a(b+c)=ab+ac so 4x + 6x = (4+6)x so the perimeter of the rectangle is
10x – 4

The perimeter of the triangle is
3x-1 + 3x + 3x+1
Here you have 3x+3x+3x -1 +1. There are two properties that allow me to do this. The commutative property for addition that a+b=b+a, and the associative property for addition that says (a+b)+c=a+(b+c). Ok, you know that -1+1=0, and because of that distributive thing again 3x+3x+3x = (3+3+3)x = 9x. You also know that 9x+0=9x So the perimeter of the rectangle is
9x

Ok this is just jumping out. What do you want to bet x = 4?
The perimeter of the triangle and rectangle are equal
9x = 10x-4
Add 4 -9x to both sides
4 = x, or, if you prefer, x = 4

Answer 3

That's a fairly basic problem.
If they are the same, they are equal, yes?
The perimeter of the rectangle is 2(2x + 3x - 2) = 10x-4
The perimeter of the triangle is 3x-1+3x+1+3x=9x
They're the same, so 10x-4=9x thus x=4
Subsitute that back into the original equations, and you have a perimeter. &)

Always remember: read the question, (unlike the people who answered before me). The question calls for the perimeter, not the value of x, hence you need to use x to work out the perimeter.

Answer 4

You know that you have to add all the sides, so why don't you do it?

The perimeter is the distance all around.
Perimeter of rectangle = 2x + 2x + 3x-2 + 3x-2
= 10x - 4

Perimeter of triangle = 3x-1 + 3x+1 + 3x = 9x

Since the perimeters are the same
9x = 10x - 4
x = 4

Answer 5

Perimeter of rect. = 2(2x + 3x - 2) = 2(5x - 2) = 10x - 4
Perimeter of triangle = 3x -1 + 3x + 1 + 3x = 9x
9x = 10x - 4
x = 4

so perimeter = 9 * 4 = 32

Answer 6

x=4

Answer 7

4

Answer 8

Prect=2(2x+3x-2)=2(5x-2)=10x-4

Ptri=3x-1+3x+1+3x=9x so
10x-4=9x subtract 9x from each side
x-4=0 add 4 to each side
x=4

check
Prect=2(2*4+3*4-2)=2(8+12-2)=2(18)=36

Ptri=3*4-1+3*4+1+3*4=9*4=36

Answer 9

2x + 2x + 3x - 2 + 3x - 2

"like terms" can be collected.
how many x's do you have, count them 2,2,3,3 x's = 10x
we have -2 and -2 which is -4
10x - 4

triangle 3x-1 + 3x+1 + 3x
we have 3,3,3 x's which is 9x
the plus one and minus one leave no constant(0)
9x

Set them equal and solve
10x - 4 = 9x
add four both sides
10x = 9x + 4
subtract 9 both sides
x=4


to get the perimeter plug into either shape(same) x=4
9x = 9(4) = 36

x=4 and perimeter=36
=]


good luck!

Answer 10

Rectangle
P = 4x + 6x - 4
P = 10x - 4
Triangle
P = 9x
10x - 4 = 9x
x = 4