Two rectangle have an area of 630cm2 each. the difference in length of rectangle is 5cm and thier width is 3cm. find dimensions of rectangle.
xy=630
(x-3)(y+5)=630
You can solve that, or note that 630 = 21*30 = 18*35
To find the dimensions of the rectangles, let's assign variables to represent the length and width of each rectangle.
Let's assume:
Length of Rectangle 1 = L1
Width of Rectangle 1 = W1
Length of Rectangle 2 = L2
Width of Rectangle 2 = W2
Given information:
Area of Rectangle 1 = 630 cm^2
Area of Rectangle 2 = 630 cm^2
Difference in length = 5 cm
Width = 3 cm
The formulas for calculating the area of a rectangle is:
Area = Length x Width
From the given information, we can form two equations:
Equation 1: Area of Rectangle 1 = L1 x W1 = 630 cm^2
Equation 2: Area of Rectangle 2 = L2 x W2 = 630 cm^2
We are also given that the difference in length is 5 cm, so we can form another equation:
Equation 3: L2 - L1 = 5 cm
Now, let's use these equations to solve for the dimensions of the rectangles:
Step 1: Solve Equation 3 for L2:
L2 = L1 + 5 (by adding L1 to both sides)
Step 2: Substitute the value of L2 in Equation 2:
(L1 + 5) x W2 = 630
Step 3: Simplify Equation 2:
W2 = 630 / (L1 + 5)
Step 4: Substitute the value of W2 in Equation 1:
L1 x (630 / (L1 + 5)) = 630
Step 5: Solve Equation 4 for L1:
Multiply both sides by (L1 + 5):
L1 x (630 / (L1 + 5))(L1 + 5) = 630(L1 + 5)
Simplify the fraction:
L1 x 630 = 630(L1 + 5)
Step 6: Distribute on both sides:
630L1 = 630L1 + 3150
Step 7: Simplify the equation:
630L1 - 630L1 = 3150
Step 8: 3150 = 0
Since we cannot solve 0 = 3150, it appears that there was an error in the given information or in our calculations. Please double-check the problem statement and try the calculations again.