a corner lot that was originally square lost 185m^2 area when one of the adjacent streets was widened by 3m and the other was widened by 5m. find the new dimensions of the lot.(hint:let x equal the length of a side of the original square lot)
It might help to draw a diagram. That's difficult to do here, so I'll set up the equation and see if you can figure it out from there.
Equation:
3(x - 5) + 5x = 185
Solve for x. Once you have x, you can determine the new dimensions of the lot.
Remember that x will equal the length of one side of the original square lot.
Bye
To solve the equation, we can follow these steps:
1. Expand the equation:
3(x - 5) + 5x = 185
3x - 15 + 5x = 185
2. Combine like terms:
3x + 5x - 15 = 185
8x - 15 = 185
3. Move the constant term to the other side of the equation:
8x = 185 + 15
8x = 200
4. Solve for x by dividing both sides by 8:
x = 200/8
x = 25
Now that we have found the value of x, which is the length of one side of the original square lot, we can determine the new dimensions of the lot.
The original square lot had all sides measuring 25 meters. Since one adjacent street was widened by 3 meters and the other by 5 meters, the new length of two adjacent sides would be:
25 + 3 = 28 meters (one side widened by 3 meters)
25 + 5 = 30 meters (the other side widened by 5 meters)
Therefore, the new dimensions of the lot would be 28 meters and 30 meters.