An area/perimeter question...?

Question

A rectangle with a perimeter 104 centimeters has a width 18cm less than it's length. What is the area? Please show the algebraic formula, and what you did, and explain, please. ^_^

Answer 1

2x+2y = 104

x+18 = y

2x+2(x+18)=104

2x+2x+36 =104

4x =104-36

4x = 68

x=17

y=35

Area= xy
= 17x35
= 595

Answer 2

Get a pen and a sheet of paper first off. Then draw you a nice rectangle.

Label the length as 'x' and the width as 'x-18'. Now set your perimeter, 104, equal to 2*l*w.
104=2x+2x-18)
Distribute the 2 to the (x-18) and you should have:
104=2x+x-36
Add the 3 to both sides to move it across and you should have
104+36=2x+2x
Combine like terms. This leaves you with:
140=4x
Divide by 4 and you get:
35=x

Now, plug that back into your rectangle, and you should g e demensions as
length=35
width=17
Multiply those two together and you get your area to be:
35*17=595cm.


Hope you understood all of this. Good luck!

Answer 3

Perimeter is the total length of all four sides. Perimeter = 2*width + 2* length. The sides are multiplied by two because they are equal (since it is a rectangle). W = L - 18. Since the width is 18 cm less, this means to subtract it (from the length as indicated). Now we replace the 'W' in our original equation (P = 2W + 2L) with our new equation (W = L-18). So... (P = 104 as indicated) 104 = 2*(L-18) + 2L. Now we solve for L. 104= 2L - 36 + 2L (collect like terms), 104 = 4L-36 (add 36 to both sides), 140=4L (divide both sides by 4), L = 35. So... W = 35 -18 = 17. Area = Length * Width. A = 35 * 17 = 595cm

Answer 4

Let L be the length and W be the width. Then we know that W = L - 18. The perimeter is 2L + 2W so

2L + 2(L - 18) = 104

2L + 2L - 36 = 104

4L = 140

L = 35

So W = 35 - 18 = 17

The area is A = LW, so

A = (35 cm)(17 cm) = 595 sq. cm.

Answer 5

_____=52
2/ 104

52-18cm=34cm
devide the perimeter by two = 52
one side you know is 18 so you subtract 18 from 52 =34 cm multiply 34 x 18 =612 square cm