If the difference between the length and breadth of a rectangle is 30 m and its perimeter is 100 m, then calculate the area of the rectangle.A400 m squareB350 m squareC450 m squareD300 m square
Question
If the difference between the length and breadth of a rectangle is 30 m and its perimeter is 100 m, then calculate the area of the rectangle.A400 m squareB350 m squareC450 m squareD300 m square
Solution
Let's solve this step by step:
Step 1: Let's denote the length of the rectangle as L and the breadth as B. According to the problem, L - B = 30.
Step 2: The perimeter of a rectangle is given by the formula 2*(L + B). According to the problem, 2*(L + B) = 100.
Step 3: From the perimeter equation, we can simplify to find that L + B = 50.
Step 4: Now we have a system of two equations: L - B = 30 and L + B = 50. We can solve this system to find the values of L and B.
Step 5: By adding these two equations, we get 2L = 80, so L = 40.
Step 6: Substituting L = 40 into the equation L + B = 50, we get B = 50 - 40 = 10.
Step 7: The area of a rectangle is given by the formula LB. Substituting L = 40 and B = 10, we get Area = 4010 = 400 m square.
So, the answer is A400 m square.
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