18. A region has an area of 42 square meters. It must be divided into the threesubregions so that the second has twice the area of the first, and the third has twicethe area of the second. Find the area of each subregion.

Accepted Solution

Answer:Area of the first region is 6 square meters.Area of the second region is 12 square meters.Area of the third region is 24 square meters.Step-by-step explanation:Given:Total area of the region, [tex]A=42\textrm{ }m^{2}[/tex]Let area of the first region be [tex]x[/tex].As per question,Area of second region is twice the first. So, area, [tex]A_{2}=2x[/tex]Area of third region is twice the second. So, area, [tex]A_{3}=2A_{2}=2(2x)=4x[/tex]Now, total area is the sum of the areas of the three regions. So,[tex]x+A_{2}+A_{3}=A\\x+2x+4x=42\\7x=42\\x=\frac{42}{7}=6\textrm{ }m^{2}[/tex]Therefore, area of first region is [tex]6\textrm{ }m^{2}[/tex]Area of second region is, [tex]A_{2}=2x=2\times 6 = 12\textrm{ }m^{2}[/tex]Area of third region is, Β [tex]A_{3}=4x=4\times 6 = 24\textrm{ }m^{2}[/tex]