If the area of the large rectangle is 147 units squared, what is the perimeter of the shaded area.
There is a visual of a large rectangle divided into four smaller ones. One is shaded. The area is given for the other three: 48 and 15 along the top half of the large rectangle and shaded area plus 28 on the bottom half.
I tried adding up the different known areas and subtracting it from 147 but 56 makes no visual sense looking at the picture. HELP!!
This problem is killing me. Thank you!
To find the perimeter of the shaded area, we first need to find the dimensions of the shaded rectangle. Let's label the dimensions of the shaded rectangle as length 'a' and width 'b'.
From the given information, we know the areas of the three non-shaded rectangles:
- The top-left rectangle has an area of 48 square units, so its length multiplied by its width must equal 48.
- The top-right rectangle has an area of 15 square units, so its length multiplied by its width must equal 15.
- The bottom rectangle has an area of 28 square units, so its length multiplied by its width must equal 28.
In the top half of the large rectangle, we have the sum of the areas of the top-left rectangle and the top-right rectangle, which makes 48 + 15 = 63 square units.
Therefore, the area of the shaded rectangle in the bottom half of the large rectangle is 147 - 63 = 84 square units.
Now, let's solve for the dimensions of the shaded rectangle using the given areas:
- We can find the length 'a' of the shaded rectangle by dividing the area 84 by the width 'b' which gives us a = 84/b.
- The total width of the shaded rectangle plus the top-right rectangle is the same as the total width of the top half of the large rectangle, which is b + width of the top-right rectangle = b + 15.
Now, let's substitute this information into the total area of the large rectangle equation:
147 = (b + 15)(a + b + 15)
Simplifying this equation will give us the value of 'b' and 'a', which are the dimensions of the shaded rectangle.
Once we have the length 'a' and width 'b' of the shaded rectangle, we can find the perimeter by using the formula P = 2(a + b).