Question

A l-meter steel rod is bent into a rectangle so that its length exceeds quadruple its width

by 5 cm. What are the dimensions of the newly formed rectangle?

Answer 1

The dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

Explanation:

Given,

A 1 meter steel rod is bent into a rectangle.

That means the perimeter of the rectangle is 1 meter.

So, Perimeter =
`1\ m=100\ cm`

Let the width of the rectangle be 'x'.

Now According to question, length exceeds quadruple its width by 5 cm.

Hence framing the above sentence in equation form, we get;

`Length=4x+5`

Now we use the formula of perimeter of rectangle,

`Perimeter=2(Length+width)`

On substituting the values, we get;

`2(4x+5+x)=100\\\\(5x+5)=(100)/(2)\\\\5x+5=50\\\\5x=50-5\\\\5x=45\\\\x=(45)/(5)=9`

Now, we substitute the value of x to get the value of length;

`Length=4x+5=4*9+5=36+5=41\ cm`

Thus, Width=9 cm Length=41 cm

Hence the dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.