In the figure Shown,two identical squares are inscibed in the rectangle.if the area of the rectangle is 36 Sq. Units,then what is the perimeter of each Square??
i dont have its answer
help
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi sana.noor,
In the drawing that you provided, you should notice that:
the width of the rectangle = 2(square's diagonal)
the height of the rectangle = 1(square's diagonal)
Using square "rules", the diagonal = x(root2)
So the area of the rectangle = (width)(height) = 2(x(root2))^2 = 36
Let's simplify:
(x(root2))^2 = 18
x^2(2) = 18
x^2 = 9
x = 3
So the perimeter of each square = 3(4) = 12
GMAT assassins aren't born, they're made,
Rich
In the drawing that you provided, you should notice that:
the width of the rectangle = 2(square's diagonal)
the height of the rectangle = 1(square's diagonal)
Using square "rules", the diagonal = x(root2)
So the area of the rectangle = (width)(height) = 2(x(root2))^2 = 36
Let's simplify:
(x(root2))^2 = 18
x^2(2) = 18
x^2 = 9
x = 3
So the perimeter of each square = 3(4) = 12
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here's a slightly different approach:
Since the height of the rectangle and the diagonal of a square are the same length, let's let x = height of rectangle
Since the width of the rectangle is equal to the length of two square diagonals, then the width of the rectangle = 2x.
The area of the rectangle is 36.
So, (base)(height) = 36
(2x)(x) = 36
2x²= 36
x²= 18
x = √18
NOTE: There's no need to simplify √18 at this point (you'll see why shortly)
If the height of the rectangle is √18, then the length of the red line (shown below) must equal √18/(2)
Likewise, the other red line has length √18/(2)
If we let y = the length of the hypotenuse, then the Pythagorean Theorem states that...
Now solve this equation for y.
If y = 3, then the perimeter of one square = (4)(3) = 12
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 1:41 pm, edited 1 time in total.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi happy888,
The 'key' to this whole question is in realizing that the width and height of the rectangle can be expressed in terms of the DIAGONAL of each of the SQUARES. Are you able to follow the 'set-up' of the calculations involved?
GMAT assassins aren't born, they're made,
Rich
The 'key' to this whole question is in realizing that the width and height of the rectangle can be expressed in terms of the DIAGONAL of each of the SQUARES. Are you able to follow the 'set-up' of the calculations involved?
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Once we know that the height of the rectangle is √18, then HALF of that is (√18)/2happy888 wrote:Hi Brent,
I didn't understand why 1/4th length of the rectangle is squareroot18/2
Thanks
I hope that helps.
Cheers,
Brent
-
- Newbie | Next Rank: 10 Posts
- Posts: 5
- Joined: Sun May 07, 2017 12:31 am
I solved it in a very easy way.
Lets take side of square is x. You can see from figure, two diagonals of squares = length of rectangle.
And one diagonal of square = width of rectangle.
So, as Length x Width = 36,
we can say (2 * root2x)* (root2x) = 36
x = 3
Perimeter of square = 12
Lets take side of square is x. You can see from figure, two diagonals of squares = length of rectangle.
And one diagonal of square = width of rectangle.
So, as Length x Width = 36,
we can say (2 * root2x)* (root2x) = 36
x = 3
Perimeter of square = 12
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Nice approach! For anyone needing a visual, this is the same approach the great Brent uses above.hotcool030 wrote:I solved it in a very easy way.
Lets take side of square is x. You can see from figure, two diagonals of squares = length of rectangle.
And one diagonal of square = width of rectangle.
So, as Length x Width = 36,
we can say (2 * root2x)* (root2x) = 36
x = 3
Perimeter of square = 12
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
The squares just take up half the rectangle. There are a few ways to see that. For example, if you divide up the picture into a grid of 8 squares, as I did below, you can see that half of each grid zone is taken up by part of a square, and the other half is taken up by non-square.
So the area of the squares is half the total area of the rectangle, so the area of the two squares is 36/2 = 18, and the area of each square is 9. So the squares measure 3 by 3, and the perimeter of each is 12.
So the area of the squares is half the total area of the rectangle, so the area of the two squares is 36/2 = 18, and the area of each square is 9. So the squares measure 3 by 3, and the perimeter of each is 12.
- Attachments
-
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Neat follow up question for anyone who wants to delve further into similar ideas:
https://www.beatthegmat.com/triangle-in ... 16268.html
https://www.beatthegmat.com/triangle-in ... 16268.html
-
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Thu Sep 14, 2017 4:33 am
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780