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1 year ago

19. Bella is putting down patches of sod

Mathematics

1 answer:

Fofino [41]1 year ago

3 0

Answer:

The dimensions of the two different rectangular regions are;

1st Arrangement:

W = 4 yards and L = 5 yards or W = 5 yards and L = 4 yards

2nd Arrangement:

W = 2 yards and L = 10 yards or W = 10 yards and L = 2 yards

The perimeter of the two different rectangular regions are;

1st Arrangement:

P₁ = 18 yards

2nd Arrangement:

P₂ = 24 yards

Step-by-step explanation:

Bella is putting down patches of sod to start a new lawn.

She has 20 square yards of sod.

We are asked to provide the dimensions of two different rectangular regions that she can cover with the sod.

Recall that a rectangle has an area given by

Area = W*L

Where W is the width of the rectangle and and L is the length of the rectangle.

Since Bella has 20 square yards of sod,

20 = W*L

There are more than two such possible rectangular arrangements.

Out of them, two different possible arrangements are;

1st Arrangement:

20 = (4)*(5) = (5)*(4)

Width is 4 yards and length is 5 yards or width is 5 yards and length is 4 yards

2nd Arrangement:

20 = (2)*(10) = (10)*(2)

Width is 2 yards and length is 10 yards or width is 10 yards and length is 2 yards

Therefore, the dimensions of two different rectangular regions are;

1st Arrangement:

W = 4 yards and L = 5 yards or W = 5 yards and L = 4 yards

2nd Arrangement:

W = 2 yards and L = 10 yards or W = 10 yards and L = 2 yards

What is the perimeter of each region?

The perimeter of a rectangular shape is given by

P = 2(W + L)

Where W is the width of the rectangle and and L is the length of the rectangle.

The perimeter of the 1st arrangement is

P₁ = 2(4 + 5)

P₁ = 2(9)

P₁ = 18 yards

The perimeter of the 2nd arrangement is

P₂ = 2(2 + 10)

P₂ = 2(12)

P₂ = 24 yards

So the perimeter of the 1st arrangement is 18 yards and the perimeter of the 2nd arrangement is 24 yards.

Note:

Another possible arrangement is,

20 = (1)*(20) = (20)*(1)

Width is 1 yard and length is 20 yards or width is 20 yards and length is 1 yard.

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Answer:

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1 year ago

There are some nickels dimes and quarters in a large piggy bank for every two nickels there are 3 dimes for every two dimes that

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We are given

piggy bank has nickels , dimes and quarters

Let's assume

number of nickels =n

every two nickels there are 3 dimes

so, number of dimes are

$=\frac{3}{2}n$

$=1.5n$

every two dimes that are 5 quarters there

so, number of quarters are

$=\frac{5}{2}\times 1.5n$

$=3.75n$

so, total number of coins = number of nickels + number of dimes +number of quarters

total number of coins =n+1.5n+3.75

there are 500 coins

so, we get

$n+1.5n+3.75n=500$

now, we can solve for n

$6.25n=500$

divide both sides by 6.25

so, we get

$n=80$

number of dimes is 1.5n

$=1.5\times 80$

$=120$

number of quarters is 3.75n

$=3.75\times 80$

$=300$

so,

Number of nickels =80

Number of dimes =120

Number of quarters =300............Answer

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