If area of a rectangle is 200 cm square and its perimeter is 60 cm find length and breadth?

Question

Answer

Answer

2(l+b)=60.. so,l+b=30..b=(30-l)... lb=200..l(30-l)=200..l^2-30l+200=0..l^2-20l-10l+200=0...l(l-20)-10(l-20)=0..(l-20) (l-10)=0..so,l=20 or 10..b= ...??

Answer

Answer

**Problem Analysis**

We are given the area and perimeter of a rectangle and we need to find the length and breadth.

Let's assume the length of the rectangle is L and the breadth is B.

We have two equations based on the given information:
1. Area of the rectangle = Length * Breadth
2. Perimeter of the rectangle = 2 * (Length + Breadth)

We can solve these equations simultaneously to find the values of L and B.

**Solution**

We are given that the area of the rectangle is 200 cm² and the perimeter is 60 cm.

Let's substitute these values into the equations and solve them simultaneously.

1. Area of the rectangle = Length * Breadth
200 = L * B ---(Equation 1)

2. Perimeter of the rectangle = 2 * (Length + Breadth)
60 = 2 * (L + B) ---(Equation 2)

Now, we have two equations with two variables. We can solve them simultaneously to find the values of L and B.

**Solving the Equations**

Equation 2 can be simplified:
60 = 2L + 2B
Divide both sides by 2:
30 = L + B ---(Equation 3)

Now, we have two equations:
200 = L * B ---(Equation 1)
30 = L + B ---(Equation 3)

We can solve these equations using substitution or elimination method.

Let's use the substitution method:
From Equation 3, we have:
B = 30 - L

Substitute this value of B into Equation 1:
200 = L * (30 - L)
200 = 30L - L²
Rearrange the equation:
L² - 30L + 200 = 0

This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's solve it using factoring:

(L - 10)(L - 20) = 0

So, either (L - 10) = 0 or (L - 20) = 0

If L - 10 = 0, then L = 10
If L - 20 = 0, then L = 20

Now, substitute the values of L back into Equation 3 to find the corresponding values of B:

For L = 10:
B = 30 - L
B = 30 - 10
B = 20

For L = 20:
B = 30 - L
B = 30 - 20
B = 10

**Conclusion**

Therefore, the length and breadth of the rectangle can be either:
Length = 10 cm, Breadth = 20 cm
or
Length = 20 cm, Breadth = 10 cm

These are the two possible solutions based on the given area and perimeter of the rectangle.

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