Question

A rectangle is 4 times longer than it’s width. The perimeter of the rectangle is 30 cm. Find the dimensions?

Answer 1

`1=12`

`w=3`

Explanation:

.

Let `l=` length and `w=` width.

Perimeter of the rectangle is:

`P=2(l+w)`

Since `l=4w`, we can substitute:

`P=2(4w+w)=2(5w)=10w`

`30=10w`

`w=3`

`l=4w=4(3)=12`

Answer 2

a=12 cm and b=3 cm

Explanation:

Let length be a
width be b

Length is Four times breadth
a=4b

Perimeter is 30 cm
Perimeter of a rectangle= a+b+a+b =2(a+b)
2(a+b)=30
Divide both sides by 2
a+b=15

a+b=15 and we know a=4b so in place of a we can write 4b i.e a+b=15 and 4b + b=15 are one and a same thing

4b+b=15
5b=15
(divide both sides by 5)
b=3

we got the value of b as 3 and we know that value of a is equal to 4 times the value of b

a=4b = `4*3` = 12

Thus a=12 cm and b=3 cm

Answer 3

The dimensions of the rectangle are `color(red)3`cm by `color(green)12`cm

Explanation:

First, write what we are given, algebraically.

Let `color(red)w` be the width of the rectangle, `l` be the length of the rectangle, and `P` be the perimeter of the rectangle.

`color(green)l = 4color(red)w`

`color(blue)P = 30`

We can now use the formula for the perimeter of a rectangle, given the length and width.

`color(blue)P = 2color(red)w + 2color(green)l`

Now, substitute in everything that we know and solve.

`color(blue)30 = 2color(red)w+2(color(green)(4w))`

`30 = 2w + 8w`

`30 = 10w`

`3 = w`

`color(red)w = 3`

It is crucial that we actually answer the question. We must find the dimensions and not just the width in centimetres. Fortunately, we know what the length is relative to the width.

`color(green)l = 4color(red)w`

`color(green)l = 4*color(red)3`

`color(green)l = 12`

Remember that the unit is centimetres. The dimensions of the rectangle are `color(red)3`cm by `color(green)12`cm