Respuesta :

jtvatsim
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!

Answer:

the length of the rectangle is 10 cm

Step-by-step explanation:

Perimeter of a rectangle is given by:

[tex]P= 2(l+w)[/tex]           ....[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.

⇒[tex]l = w+4[/tex]

It is also given that the the perimeter is 32 cm

⇒P= 32 cm

then substitute these in [1] we get

[tex]32 =2(w+4+w)[/tex]

Combine like terms;

[tex]32 =2(2w+4)[/tex]

Divide both sides by 2 we get;

[tex]16 =2w+4[/tex]

Subtract 4 from both sides we get;

[tex]12=2w[/tex]

Divide both sides by 2 we get;

w = 6 cm

then;

[tex]l = 6+4=10[/tex] cm

Therefore, the length of the rectangle is 10 cm

Otras preguntas