112k views
2 votes
a number of coins can be placed in a square 14 coins per side. also, be arranged in a rectangular array with 21 more coins in the length than in the width. How many coins are on the length and width of the rectangular array a number of coins can be placed in a square array with 14 coins per side?​

1 Answer

3 votes

Answer:

Explanation:

Let's start with the square array. The total number of coins in the square is the area of the square, which is (14 coins per side)^2 = 196 coins.

For the rectangular array, let's use "x" to represent the width (in coins) and "x+21" to represent the length (in coins). The total number of coins in the rectangular array is the product of the length and width, which is:

x(x+21) = x^2 + 21x

We don't know the exact number of coins in the rectangular array, but we do know that it's greater than or equal to 196 (the number of coins in the square array). So we can write:

x^2 + 21x >= 196

Now we can solve for x:

x^2 + 21x - 196 >= 0

We can factor this quadratic equation:

(x+28)(x-7) >= 0

The solutions are x <= -28 or x >= 7. However, since x represents the width (a positive quantity), we can ignore the negative solution. So we have:

x >= 7

This means that the width of the rectangular array must be at least 7 coins. To find the length, we can use x+21. If we make x=7, then the length would be 7+21=28. So the rectangular array would have 7 coins on the width and 28 coins on the length.

User Kree
by
7.6k points