Question

HELP!!! PLEASE!! I'm very stupid, unfortunately, and I do not know how to answer this.

The width of a rectangle is 8 cm less than its length. The perimeter of the rectangle is 52 cm.

What is the width of the rectangle?

7 cm

9 cm

15 cm

17 cm

Answer 1

@mathmale Please help :(

Answer 2

Perimeter = width + width + length + length :)

52cm = x + x + (x+8) + (x+8) "Width is 8cm less than length"
52cm = 4x + 16 Combining Like-terms (simplifying)
36 = 4x Subtraction Property of Equality
9 = x Division Property of Equality

Answer: 9cm.

Answer 3

Where did the x come in on length times length??

Answer 4

This being algebra, you need to represent unknown quantities with letters, such as x, y, z, P (for perimeter), A (for area), and so on.

Answer 5

I'd recommend that you use letters such as l and w to represent length and width.

Answer 6

I know that, but I do not understand the (x + 8) + (x +8).

Answer 7

I would have thought it would solely be 8 + 8.

Answer 8

Since the width is 8cm less than the length, I represented the width as x, and since the length is 8cm bigger than the width, I represented it as x+8.

Answer 9

"The width of a rectangle is 8 cm less than its length:" If w represents the width and l the length, then w=l-8 [all in cm]. (Generally the width is less than the length.)

Answer 10

Can someone greatly explain this to me???

Answer 11

@mhchen @mathmale @Vuriffy

Answer 12

Even if I would have remembered the equation, P = 2w + 2l, I would not have thought of combining 4 X's and doing what @mhchen did

Answer 13

Please guys @mathmale @mhchen @Vuriffy

Answer 14

PLEASE I need to finish this I'm so tired

Answer 15

I'm so stupid that I can't even figure this out on my own

Answer 16

Okay look, so the width is 8cm less than the length right? If we represented the width with x, then the length is x+8. Get it?

OR by the same logic, we can make the width x-8 and the length as x. Same thing, got it?

We just apply this to the formula you just wrote. P=2l+2w

Answer 17

Another way at going at this is by using that x+8 but plugging in values.

Answer 18

Let's try 7.
(7+8)+(7+8)+(15-8)+(15-8)
44 = 52. Incorrect.

Answer 19

But if it's 9. then isn't it 9 + 9 = 18 and 8 + 8 = 16?? That's not 52

Answer 20

Or am I going about this totally wrong?

Answer 21

Let's try 9.
(9+8)+(9+8)+(17-8)+(17-8)
17 + 17 + 9 + 9
52 = 52.

Answer 22

You may figure out an equation then plug in values from the answers to swiftly find what you are looking for.

Answer 23

A rectangle has 4 sides; two sides have the same value.

Answer 24

I don't get why we have to do 9 + 8 *2 and then 17 + 8 *2 I don't get it

Answer 25

As aforementioned, a rectangle has 4 sides.
Two sides of the rectangle have the same value, and the other two sides of the rectangle have the same value.

Answer 26

Earlier I suggested that you represent the width by l-8, since the width is "8 less than the length."

The perimeter is given; it is 52 cm. The perimeter is the sum of 2 l and 2 w.

Write this as an equation, please.

Answer 27

Which is why the value is there twice.
(17 + 17) + (9 + 9)

Answer 28

Once again: The formula for perimeter is P = 2 l + 2 w (where 'l" signifies length)