is Any math genius here who can answer above question correctly
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is Any math genius here who can answer above question correctly
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Question 1 :-
Answer :-
Given :-
To find :-
Step-by-step explanation :-
Detailed explanation of the solution :-
Let's understand!
The question has given us the Length and Breadth of the park. We have to find the cost of fencing all around the park at the rate of Rs 15 per meter. Since we have to find the cost of fencing all around the park, therefore we will find the perimeter of the rectangle and not the area. Then we will find the cost of fencing by multiplying the rate of fencing per meter with the perimeter.
We know that :-
Perimeter of a rectangle = 2 (L + B)
Let's use this formula to find the perimeter by substituting the values given in the question.
Here,
Length = 30 m.
Breadth = 20 m.
So,
Removing the brackets,
Adding the numbers,
Since we found the perimeter of the rectangle,
Therefore now let's find the cost of fencing all around the park.
Rate of fencing = Rs 15 per meter.
So, cost of fencing = Rs 15 × 100 = Rs 1500.
Thus, the cost of fencing all around the park at the rate of Rs 15 per meter is Rs 1500
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Question 2 :-
Answer :-
Given :-
To find :-
Step-by-step explanation :-
Detailed explanation of the solution :-
Let's understand!
The question has given us the perimeter of the rectangle. We also know that the square and the rectangle have the same perimeter, which is 100 cm. Now using this information, we will first find out the side of the square, and then use it to find the breadth of the rectangle by subtracting 2 cm from it (Since the breadth of the rectangle is 2 cm less than the side of the square). At last, we will use the breadth and the perimeter of the rectangle to find it's length by applying the formula required for finding the perimeter of a rectangle.
The perimeter of the square and the rectangle is the same.
We know that :-
Perimeter of a square = Side × Side.
The side of the square is 10 cm.
It has been given that the breadth of the rectangle is 2 cm less than the side of the square.
Here,
Side of the square = 10 cm.
So, the Breadth of the rectangle is 8 cm.
Since we have the Breadth now,
Therefore let's find the Length of the rectangle using the formula required for finding the perimeter of a rectangle.
We know that :-
Perimeter of a rectangle = 2 (Length + Breadth)
Now let's apply this formula and find the Length by substituting the given values in the formula.
Let's assume that the Length is l.
Here,
Breadth = 8 cm.
Perimeter = 100 cm.
So,
Removing the brackets,
Transposing 16 from LHS to RHS, changing it's sign,
Subtracting the numbers,
Transposing 2 from LHS to RHS, changing it's sign,
Dividing 84 cm by 2,
So, the length of the rectangle is 42 cm.
Let's solve the questions one by one!
Analysis:
The dimensions of a rectangular park are 30 m by length and 20 m by breadth. Fencing has to be done in the park. And the cost of fencing the park per metre is ₹15. We're asked to find the cost of fencing the park at the above mentioned rate.
Solution:
As per the analysis we should find the cost of fencing. We know that, fencing is only done in boundaries of any place. So, to find the total length of the boundary, we have to find the “perimeter of the rectangular field”.
On substituting the measures:
Since the perimeter of the park is 100 m, the “cost of fencing” equals:
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Now, let's step into the second question!
Analysis:
The perimeter of a rectangle and a square equals the same, i.e, 100 cm. The breadth of the rectangle equals the value when we subtract two from the measure of side. We're asked to find the side of square and measures of length and breadth of the rectangle.
Solution:
Generally, the question "Which to find first? (The side of the square or the dimensions of the rectangle)" arises. The out-and-out answer for this is "finding the side of the square as first". Why? Because, the breadth of the rectangle is dependent on the side of the square. Hence, this has to be found first.
↪️Side of the square:
As the measure of perimeter is given, the length of its side can be obtained by substituting the given measure in its formula.
Now, we know the side of the square and the condition to find the breadth of the rectangle. So, as per it, we shall find the breadth of the rectangle!
Since we know the measures of breadth and perimeter of the rectangle, we can find its length by substituting the known measures in the formula of perimeter of rectangle:
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