The dimension that would give the maximum area is 20.8569
<h3>How to solve for the maximum area</h3>
Let the shorter side be = x
Perimeter of the semi-circle is πx
Twice the Length of the longer side
![[70-(\pi )x -x]](https://tex.z-dn.net/?f=%5B70-%28%5Cpi%20%29x%20-x%5D)
Length = ![[70-(1+\pi )x]/2](https://tex.z-dn.net/?f=%5B70-%281%2B%5Cpi%20%29x%5D%2F2)
Total area =
area of rectangle + area of the semi-circle.
Total area =
![x[[70-(1+\pi )x]/2] + [(\pi )(x/2)^2]/2](https://tex.z-dn.net/?f=x%5B%5B70-%281%2B%5Cpi%20%29x%5D%2F2%5D%20%2B%20%5B%28%5Cpi%20%29%28x%2F2%29%5E2%5D%2F2)
When we square it we would have
![70x +[(\pi /4)-(1+\pi)]x^2](https://tex.z-dn.net/?f=70x%20%2B%5B%28%5Cpi%20%2F4%29-%281%2B%5Cpi%29%5Dx%5E2)
This gives
![70x - [3.3562]x^2](https://tex.z-dn.net/?f=70x%20-%20%5B3.3562%5Dx%5E2)
From here we divide by 2

The maximum side would be at

This gives us 20.8569
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Answer:
51
Step-by-step explanation:
12+39=51
Answer: 5
Step-by-step explanation:
Total number of wheels in the toy shop = 37 wheels
Number of wheels for tricycles = 3
Number of wheels for go-carts = 5
- Since the total number of tricycles and go-carts are not given, we solve this question using Assumption.
- Let's assume: We have 4 tricycles and 4 go-carts
(4 x 3) + (4 x 5)
= 12 + 20
= 32 wheels. This assumption is wrong.
- Let's assume: We have 4 tricycles and 5 go-carts
(4 x 3) + (5 x 5)
= 12 + 25
= 37 wheels. This assumption is correct.
Therefore, we have 4 tricycles and 5 go-carts in the toy shop.
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