如果一个矩形的长度增加 50%，宽度减少 25%，那么求其面积的变化百分比？
在我们的日常生活中，我们注意到我们周围的不同事物，它们涵盖了一些空间和体积。有些东西可能是一维的，比如绳子、线等，有些东西可能是二维的，比如平原、地板、墙壁，或者一些东西可能是三维的，比如球、圆柱体等。在测量中，当我们谈论一维时这意味着我们在计算周长时，当我们谈论二维时，我们正在谈论面积，而当我们谈论三时，我们正在计算面积。因此我们可以得出结论，测量是处理几何图形计算及其面积、周长、表面积或体积的数学分支。
让我们详细讨论与测量相关的术语。
- 周长：周长是边界长度的总和。它是一维量。它的单位就是单位本身。
- 面积：面积是周长内的空间。它是一个二维量。它的单位是（单位）²。
- 体积：体积是身体覆盖的空间量。它是一个三维量。它的单位是（单位）³。
矩形面积
The area of the rectangle is the multiplication of length and width. It is extended in two dimensions. For example: If we paint a sheet of paper and we move our hands two dimensions, either horizontal or vertical.
If the length of a rectangle is ‘l’ and the width of the rectangle is ‘b’ then the formula to calculate the area of the rectangle is:
Area = l × b
如果一个矩形的长度增加 50%，宽度减少 25%，那么求其面积的变化百分比？
解决问题的步骤：
Step 1: Suppose the length and width of the rectangle.
Let the length be ‘l’ and width be ‘b’.
Step 2: Find out the initial area.
Initial Area = l×b
Step 3: According to the question, increase or decrease the length and width of the rectangle.
It is given that length is increased by 50% and the width of the rectangle is decreased by 25%.
New Length = l × (1+50/100)
= l × (1+1/2)
= (3l)/2
New Width = b × (1-25/100)
= b × (1-1/4)
= 3b/4
Step 4: Find out the new area.
New area = new length × new width
= {(3l)/2} × (3b/4)
= (9lb)/8
Step 5: Find out the change in percent.
Change percent = {(Final Area – Initial Area)/(Initial Area)} × 100
= [{(9lb)/8 – (lb)}/(lb)] × 100
= {(lb/8)/lb} × 100
= (1/8) × 100
= 12.5%
Step 5: If the final answer is negative, it means a decrease in area and if the final answer is positive it means an increase in area.
The answer is 12.5%, which means that area is increased by 12.5%.
类似问题
问题1：如果一个矩形的长度增加50%，宽度减少50%，那么它的面积变化百分比是多少？
解决方案：
Let the length be ‘l’ and width be ‘b’.
Initial Area = l×b
It is given that length is increased by 50% and the width of the rectangle is decreased by 50%.
New Length = l×(1+50/100)
= l×(1+1/2)
= (3l)/2
New Width = b×(1-50/100)
= b×(1-1/2)
= b/2
New area = new length × new width
= {(3l)/2}×(b/2)
= (3lb)/4
Change percent = {(Final Area – Initial Area)/(Initial Area)} × 100
=[{(3lb)/4 – (lb)}/(lb)] × 100
= {(-lb/4)/lb} × 100
= (-1/4) × 100
= – 25%
The answer is -25%, which means that area is decreased by 25%.
问题2：如果一个矩形的长度增加75%，宽度减少25%，那么它的面积变化百分比是多少？
解决方案：
Let the length be ‘l’ and width be ‘b’.
Initial Area = l×b
It is given that length is increased by 75% and the width of the rectangle is decreased by 25%.
New Length = l×(1+75/100)
= l×(1+3/4)
= (7l)/4
New Width = b × (1-25/100)
= b × (1-1/4)
= 3b/4
New area = new length × new width
= {(7l)/4} × (3b/4)
= (21lb)/16
Change percent = {(Final Area – Initial Area)/(Initial Area)} × 100
= [{(21lb)/16 – (lb)}/(lb)] × 100
= {(5lb/16)/lb} × 100
= (5/16) × 100
= 31.25%
The answer is 31.25%, which means that area is increased by 31.25%.