A piece of scenery for the school play is in the shape of a 5 foot long rectangle. The designer decides to increase the length. There will be 3 identical rectangles with a total length of 17 feet. By how much did the designer increase the length of each rectangle?

Step-by-step explanation:

The school play ground is.

5ft long rectangle

The designer want to increase the length,

Then, there will be 3 identical rectangle of total length of 17ft

By how much did he increase the of each rectangle

Original, the length of the rectangle is 5ft, now, we want to design three rectangle. This three identical rectangle will have total length of (5+5+5)ft,

The original length of the three rectangle is meant to be 15ft,

Now he increase the length to 17ft,

This shows that he has increase all the three rectangle by 2ft.

So, each rectangle is expected to be increased by ⅔ft

So, he increased each rectangle length by ⅔ft.

Mathematically,

Let the increase be x

Then, he increase each length by x, so the new length is

5+x

Then, there are 3 rectangles, so their total length after increase is 3×(5+x)

And this total length after increase is give as 17ft

Then,

3(5+x) = 17

Solving this

15 + 3x = 17

3x = 17-15

3x = 2

x = ⅔ ft

So, the mathematical model of the increase is 3(5+x) = 17 and the increase is ⅔ft

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