Question

Paul has four paper strips of the same length. He glues two of them together with a 4 cm overlap, and the new strip is 36 cm long. He wants to make a 30 cm long strip with the other two strips. How long should the overlap be?

Answer 1

10 cm overlap required to make a 30 cm long strip.

Explanation:

Given:

Four paper strips of the same length.

Two of them glued together with a 4 cm overlap to make a new strip which is 36 cm long.

To find:

Overlap required to make a strip which is 30 cm long = ?

Solution:

First of all, let us understand the concept of overlap.

Please refer to the attached image.

Let length of each strip be
`x` cm.

Given that there is 4 cm overlap resulting in new strip of length 36 cm.

The overlapping length is counted only once as clear from the figure attached.

So, Let us try to find the equation:

`x +(x-4) = 36\\\Rightarrow 2x=40\\\Rightarrow x = 20\ cm`

i.e. each strip length is 20 cm.

Now, let us assume, an overlap of 'y' cm is to be made to make a new strip of 30 cm.

The equation will be:

`(20-y)+20 =30\\\Rightarrow y = 40-30\\\Rightarrow y = 10\ cm`