Question

The length of a rectangle is 4 cm greater than its width. the perimeter is 32 cm. find the length of the rectangle.

Answer 1

the length of the rectangle is 10 cm

Explanation:

Perimeter of a rectangle is given by:

`P= 2(l+w)` ....[1]

where

P is the perimeter of a rectangle

l is the length of the rectangle

w is the width of the rectangle

As per the statement:

The length of a rectangle is 4 cm greater than its width.

⇒
`l = w+4`

It is also given that the the perimeter is 32 cm

⇒P= 32 cm

then substitute these in [1] we get

`32 =2(w+4+w)`

Combine like terms;

`32 =2(2w+4)`

Divide both sides by 2 we get;

`16 =2w+4`

Subtract 4 from both sides we get;

`12=2w`

Divide both sides by 2 we get;

w = 6 cm

then;

`l = 6+4=10` cm

Therefore, the length of the rectangle is 10 cm

Answer 2

Classic Algebra/Geometry question, gotta love it.

[1] Let's first remember how to calculate perimeter of rectangles. We just add up all the sides: two lengths and two widths. P = 2*L + 2*W.

[2] Now to add Algebra to make everyone oh so happy.
Let's give the width a name, say, W (because we are SO creative). The name of the length will be L (again because we are SO creative). The length of the rectangular is 4 cm greater than the width. In symbols, we are saying
L = W + 4

We know the perimeter is 32 cm. So, P = 32.

But, wait a second, didn't I just say that P = 2*L + 2*W before? I did, that's a clue! Since P = 32, it must mean that 32 = 2*L + 2*W.

But, wait, didn't I just say that L = W + 4? I did, that's another clue! That must mean that 32 = 2*L + 2*W is the same thing as
32 = 2*(W+4) + 2*W [watch out for those parentheses!]
32 = 2*W + 8 + 2*W
32 = 4*W + 8
24 = 4*W
6 = W

So the width is 6 cm. We want the length, which is just L = W + 4 = 6 + 4 = 10. So the length is 10 cm. We are done!