1. The lenght of rectangle is greater than its breadth by 2 cm.If the length is increased by 4 cm and the breadth decreased by 3 cm ,the area remains th same . Find length and breadth of the rectangle ?
L-2=W
(L+4)(W-3)=LW
check that. So for W, put in L-2, multiply out, and solve for L.
Thank's Mr.bobpursley .
To solve this problem, we can use algebraic equations. Let's assign variables to the length and breadth of the rectangle.
Let's say the length of the rectangle is 'L' cm and the breadth is 'B' cm.
According to the problem, the length is greater than the breadth by 2 cm. So, we can write the equation:
L = B + 2 (Equation 1)
Now, if the length is increased by 4 cm and the breadth is decreased by 3 cm, the new length will be L + 4 and the new breadth will be B - 3.
The area of a rectangle is given by the formula: Area = Length × Breadth.
According to the problem, the area remains the same. So, we can write another equation:
L × B = (L + 4) × (B - 3) (Equation 2)
Now, let's substitute the value of L from Equation 1 into Equation 2:
(B + 2) × B = (B + 2 + 4) × (B - 3)
B^2 + 2B = (B + 6)(B - 3)
Expanding the right side of the equation:
B^2 + 2B = B^2 + 3B - 18
Now, simplify the equation:
2B = 3B - 18
Bringing like terms to one side:
2B - 3B = -18
-B = -18
B = 18
Now, substitute the value of B back into Equation 1 to find L:
L = B + 2 = 18 + 2 = 20
So, the length of the rectangle is 20 cm and the breadth is 18 cm.