see attached picture for partial/additional solution!
wait for picture to load, hope you can see it!
ORIGINAL SOLUTION (not copy pasted):
NOTE: The solution is a long read, but the the solution is easy once you get the logic! :)
Let's Begin!
To find Perimeter of shaded region or (as I may sometimes refer it as Rectangle 4), we need to know it's L and W
We already know Area of whole shaded region is 54 because the Area of the whole rectangle is 147.
So,
Area of Shaded Region = 147 - 48 - 15 - 28
Area of Shaded Region = 56 square units
So Area of shaded region formula is:
A = L * W
56 = L * W
and Perimeter of shaded region formula is:
Perimeter = 2(L + W)
Now let's find the the total L and W of the shaded region!
Let's start at Rectangle 2 with a given area of 15.
Let's call this Area as A2.
so A2 = 15
A2 = L * W
Now this is where all the solution comes from, you cannot solve this if you didn't see this coming!
Think of 2 numbers or factors that will result in 15.
I can think of only 2:
15 x 1 or 5 x 3
Assuming the figure shown is proportional to its measurements, then the correct answer would be 5 x 3, because 15 x 1 will make the drawing long and thin! (and later if you repeat this whole process and try to use 15 x 1, then you will find out that you will not get the total Area = 147, hence it is wrong to select 15 x 1)
So now we know the Length and Width of Rectangle 2 as
L = 5
W = 3
From the Width of Rectangle 2 which is equal to 3, we can conclude that the Width of Rectangle 1 would also be equal to 3. Since we also know the Area of Rectangle 1, then we can now solve for it's Length.
So, let's call Area of Rectangle 1 as A1.
so,
A1 = L * W
48 = L * 3
L = 48/3
L = 16
Now we know the Length of Rectangle 1 and we know the Length of Rectangle 2. And the 2 lengths add up to the whole Length of the Whole rectangle.
In short,
L of Whole Rectangle = L of Rectangle 1 + L of Rectangle 2
L of whole Rectangle = 16 + 5
L of whole Rectangle = 21
Finally we can solve for the Width of the Whole Rectangle based on the fact that the whole area was given as 147 square units.
A = L * W
147 = 21 * W
W = 147/21
W = 7
Now we have the W of whole rectangle, we can now solve the width of Rectangle 4 or the shaded region.
Width of Rectangle 4 or the shaded region is simply 7 - 3 = 4 (refer to attach picture for better visualization)
But to solve for Perimeter of Shaded Region, we are still missing its Length.
So let's get the Length of shaded region, by considering Rectangle 3.
Knowing Width of Rectangle 3 is just the same as Rectangle 4, we can now solve the Length of Rectangle 3, as the Area is given as 28.
so,
A = L * W
28 = L * 4
L = 28/4
L = 7
Finally we can get Length of Rectangle 4 or the shaded region as:
Length of Rectangle 4 = Length of Whole Rectangle - Length of Rectangle 3
Length of Rectangle 4 = 21 -7
Length of Rectangle 4 = 14
Now we can finally solve the Perimeter of Rectangle 4 or the shaded region.
Perimeter = 2(L+W)
Perimeter = 2(14+4)
Perimeter = 2(18)
Perimeter = 36 units
Hence the Perimeter of the shaded Region is 36 units
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Answers & Comments
Answer:
see attached picture for partial/additional solution!
wait for picture to load, hope you can see it!
ORIGINAL SOLUTION (not copy pasted):
NOTE: The solution is a long read, but the the solution is easy once you get the logic! :)
Let's Begin!
To find Perimeter of shaded region or (as I may sometimes refer it as Rectangle 4), we need to know it's L and W
We already know Area of whole shaded region is 54 because the Area of the whole rectangle is 147.
So,
Area of Shaded Region = 147 - 48 - 15 - 28
Area of Shaded Region = 56 square units
So Area of shaded region formula is:
A = L * W
56 = L * W
and Perimeter of shaded region formula is:
Perimeter = 2(L + W)
Now let's find the the total L and W of the shaded region!
Let's start at Rectangle 2 with a given area of 15.
Let's call this Area as A2.
so A2 = 15
A2 = L * W
Now this is where all the solution comes from, you cannot solve this if you didn't see this coming!
Think of 2 numbers or factors that will result in 15.
I can think of only 2:
15 x 1 or 5 x 3
Assuming the figure shown is proportional to its measurements, then the correct answer would be 5 x 3, because 15 x 1 will make the drawing long and thin! (and later if you repeat this whole process and try to use 15 x 1, then you will find out that you will not get the total Area = 147, hence it is wrong to select 15 x 1)
So now we know the Length and Width of Rectangle 2 as
L = 5
W = 3
From the Width of Rectangle 2 which is equal to 3, we can conclude that the Width of Rectangle 1 would also be equal to 3. Since we also know the Area of Rectangle 1, then we can now solve for it's Length.
So, let's call Area of Rectangle 1 as A1.
so,
A1 = L * W
48 = L * 3
L = 48/3
L = 16
Now we know the Length of Rectangle 1 and we know the Length of Rectangle 2. And the 2 lengths add up to the whole Length of the Whole rectangle.
In short,
L of Whole Rectangle = L of Rectangle 1 + L of Rectangle 2
L of whole Rectangle = 16 + 5
L of whole Rectangle = 21
Finally we can solve for the Width of the Whole Rectangle based on the fact that the whole area was given as 147 square units.
A = L * W
147 = 21 * W
W = 147/21
W = 7
Now we have the W of whole rectangle, we can now solve the width of Rectangle 4 or the shaded region.
Width of Rectangle 4 or the shaded region is simply 7 - 3 = 4 (refer to attach picture for better visualization)
But to solve for Perimeter of Shaded Region, we are still missing its Length.
So let's get the Length of shaded region, by considering Rectangle 3.
Knowing Width of Rectangle 3 is just the same as Rectangle 4, we can now solve the Length of Rectangle 3, as the Area is given as 28.
so,
A = L * W
28 = L * 4
L = 28/4
L = 7
Finally we can get Length of Rectangle 4 or the shaded region as:
Length of Rectangle 4 = Length of Whole Rectangle - Length of Rectangle 3
Length of Rectangle 4 = 21 -7
Length of Rectangle 4 = 14
Now we can finally solve the Perimeter of Rectangle 4 or the shaded region.
Perimeter = 2(L+W)
Perimeter = 2(14+4)
Perimeter = 2(18)
Perimeter = 36 units
Hence the Perimeter of the shaded Region is 36 units
• • • Follow, follow, follow, to get the answers that has sense, make sense, and gives you tips, tricks and more! • • • • • • Less than 7000 points... The Road to Genius Rank Level • • •✓✓✓ Follow and Hit that Brainy button. ✓✓✓