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

3 Answers
Feb 7, 2018

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

Feb 7, 2018

a=12 cm and b=3 cm

Explanation:

Let length be a
width be b

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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

Feb 7, 2018

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

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)3cm by color(green)12cm