Initially, school field is 50 meters in length with 30 meters width. After
expansion, the length increased by 20% and the area becomes 2340 square
meters, therefore the width has increased_________ meters.
new length = 1.2(50) or 60 m
new area = 2340
new width = 2340/60 = 39
increase in width = 9 m
To find the increase in width, we first need to calculate the original area of the school field.
The area of a rectangle is given by the formula: Area = length * width
Given that the original length is 50 meters and the original width is 30 meters, we can calculate the original area:
Original Area = 50 meters * 30 meters = 1500 square meters
Now, to find the increase in length, we know that the area after expansion is 2340 square meters. We were also given that the length increased by 20%.
Let's assume the increase in length is x meters.
After the expansion, the new length is 50 meters + x meters, and the new width is 30 meters + y meters.
Using the formula for area, we can set up the following equation:
(50 + x) meters * (30 + y) meters = 2340 square meters
Expanding this equation, we get:
1500 + 50y + 30x + xy = 2340
Now, we can solve this equation to find the values of x and y.
However, before we do that, let's rearrange the equation to isolate y:
50y + 30x + xy = 2340 - 1500
50y + 30x + xy = 840
Now, we need to apply the 20% increase in the length (x) to the equation. Since the original length was 50 meters, a 20% increase corresponds to 0.2 * 50 = 10 meters.
Substituting this value into the equation:
50y + 30(10) + 10y = 840
Simplifying further:
50y + 300 + 10y = 840
Combining like terms:
60y + 300 = 840
Subtracting 300 from both sides:
60y = 540
Dividing both sides by 60:
y = 9
Therefore, the width has increased by 9 meters.