Question

# A fence is put around a rectangular plot of land. The perimeter of the fence is 28 feet. Two of the opposite sides of the fence cost $10 per foot. The other two sides cost $12 per foot. If the total cost of the fence is $148, what are the dimensions of the fence?

Hint:

### let the length of plot be l and let the breadth of plot be b

Given total perimeter of the plot = 2(l + b) = 28

Given total cost of fence = cost of fencing length 1 + cost of fencing breadth b

= $148.

## The correct answer is: 1 = 10

### Ans :- 10 by 4 is the dimensions of the rectangular plot fence

Explanation :-

Step 1:- frame the system of linear equations from given conditions

let the length of plot be 1 and let the breadth of plot be b

Given total perimeter of the plot = 2(1 + b) = 28 — eq1

let the breadth b fence cost $12 per foot .

let the length 1 fence cost $10 per foot

Given total cost of fence = cost of fencing length 1 + cost of fencing breadth b

cost of fencing length 1 = 1 cost of fencing per foot .

cost of fencing length 1 = $10(1)

cost of fencing breadth b = b cost of fencing per foot

cost of fencing breadth b = $12(b)

Total cost of fencing be = 10(1) + 12b

10l + 12b = 148 5l + 6b = 74 — eq 2

Step 2 :- eliminate x to find value of y

Doing 5eq1 - eq2 to eliminate x

We get 5l + 5b = (5l + 6b) = 5(14) = 74

5l + 5b - 5l - 6b = 70 - 74

-b = -4

∴ b = 4

Step 3:- substitute the value of y in eq1 to get the value of x

∴ l = 10.

∴ we get the dimensions of rectangular plot = 10 by 4 (in foots)

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Which of the following is true about the standard deviations of the two data sets in the table above?

**Note:**

We could also calculate the standard deviation for both the data sets

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.

Which of the following is true about the standard deviations of the two data sets in the table above?

**Note:**

We could also calculate the standard deviation for both the data sets

The formula for standard deviation is

Where,

= standard deviation

= total number of terms

= terms given in the data

= mean

After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.