If the Perimeter of Square Region S and the Perimeter of Rectangular GMAT Problem Solving

Question: If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S

1. 25:16
2. 24:25
3. 5:6
4. 4:5
5. 4:9

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
Let the side of square be s and the side of rectangle a and b

Given:

The sides of R are in the ratio 2:3 --> a/b= 2/3--> b= 3a/2.
The perimeter of square region S and the perimeter of rectangular region R are equal --> P= 4s= 2(a+b) --> 2s= a+b= 5a/2 --> s=5a/4.

Question: area of R/area of S= ab/s^2= ?

Substitute b = 3a/2 and s= 5a/4 into the question: ab/s^2= 3a^2/2∗16/25a^2= 24/25.
= 24:25

Approach Solution 2:
In figure R –
Length = 3 ; Breadth = 2
Area of R = 6 and Perimeter of R = 2 ( 3 + 2 ) => 10
In figure S –
Sides = S (Say)
So, 4s = 10
Or, s = 5/2
Area of S = 25/4

Hence area of R to the area of S = 6 : 25/4 => 24 : 25

Approach Solution 3:
We know Perimeter of a square (Ps)= 4*side
Perimeter of a rectangle (Pr)= 2(length+breadth)

Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k= 5k; we can assume such a number)

Therefore,
Ps = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12

Area of the rectangle = 8*12 = 96 sq. units

Question asked= Area of the rectangle : Area of the square = 96:100 ==> 24:25

“If the perimeter of square region S and the perimeter of”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

Suggested GMAT Problem Solving Samples

• Which of the following represents the largest 4 digit number GMAT Problem Solving
• The Lengths of the Sides of an Obtuse-Angled Triangle are x, y, and z, Where x, y and z are Integers GMAT Problem Solving
• If the expression sqrt2+2+2+2+ ... extends to an infinite number of roots GMAT Problem Solving
• How Many Different Lines Are Determined by 4 Distinct Points in a Plane If No 3 GMAT Problem Solving
• If The Diagonal of Rectangle Z is d, And The Perimeter of Rectangle Z is p GMAT Problem Solving
• 99,999^2−1^2 = ? GMAT Problem Solving
• How Many of The Three-Digit Numbers Are Divisible by 7? GMAT Problem Solving
• In a Camp, There is a Meal for 120 Men or 200 Children GMAT Problem Solving
• As Part Of a Game, Four People Each Must Secretly Choose an Integer Between 1 and 4 GMAT Problem Solving
• If Integer p is a Factor of 42, is p a Prime Number? GMAT Problem Solving
• A Triangle in the xy-Coordinate Plane Has Vertices With Coordinates (7, 0), (0, 8), and (20, 10) GMAT Problem Solving
• A Regular Hexagon is Inscribed in a Circle, What is the Ratio of the Area of the Hexagon GMAT Problem Solving
• √9+√80+√9−√80) 2 GMAT Problem Solving
• What Is The Circumference Of The Semicircle In The Figure Shown? GMAT Problem Solving
• In a Trapezium ABCD, AB Is Parallel To DC, AB = 3*DC, And The Diagonals Of The Trapezium Intersect At O GMAT Problem Solving
• A Bag Contains 5 Red Balls And Some Blue Balls GMAT Problem Solving
• A Small Water Pump Would Take 2 Hours To Fill An Empty Tank GMAT Problem Solving
• ABCD Is An Isosceles Trapezium GMAT Problem Solving
• An Equilateral Triangle is Constructed on Each Side of a Square GMAT Problem Solving
• For A Negative Integer x, What Is The Value Of x * √(x^2)? GMAT Problem Solving
• Five Letters Are To Be Placed Into Five Addressed Envelopes GMAT Problem Solving
• Find The Number Of Trailing Zeros In The Product Of (1^1) GMAT Problem Solving
• Find The Altitude Of An Equilateral Triangle Whose Side is 20 GMAT Problem Solving
• Which of the following is the value of√3√0.000064? GMAT Problem Solving
• Two Dice are Thrown Simultaneously. What is the Probability of Getting Two Numbers Whose Product is Even? GMAT Problem Solving
• The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving
• Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving
• An Express Train Traveled At An Average Speed of 100 Kilometers Per Hour GMAT Problem Solving
• If m Lies Between The Integers p and s On the Number Line Shown GMAT Problem Solving
• A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
• If x^2 − 5x − 6 = 0, which of the following could be x ? GMAT Problem Solving
• How Many Numbers Between 1 and 1000, Inclusive Have an Odd Number of Factors? GMAT Problem Solving
• Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ? GMAT Problem Solving
• Which Among the Following is the Smallest 7-digit Number that is Exactly Divisible by 43? GMAT Problem Solving
• During a Trip, Francine Traveled x Percent of the Total Distance at an Average Speed of 40 Miles GMAT Problem Solving
• Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
• Which of the following is greatest? GMAT Problem Solving
• The Cost Price of 20 Articles is The Same as The Selling Price of x Articles GMAT Problem Solving
• In The Figure Shown, If The Area of The Shaded Region is 3 Times The Area of The Smaller Circular Region GMAT Problem Solving
• A Regular Hexagon has a Perimeter of 30 units GMAT Problem Solving
• All the Numbers 2, 3, 4, 5, 6, 7 are Assigned to the Six Faces of a Cube, One Number to Each Face GMAT Problem Solving
• If it is true that x > -2 and x < 7, which of the following must be true? GMAT Problem Solving
• In a Certain Store, the Profit is 320% of the Cost GMAT Problem Solving
• If y is the Smallest Positive Integer Such That 3,150 Multiplied By y is the Square of an Integer GMAT Problem Solving
• If mn ≠ 0 and 25 Percent of n Equals 37 1/2 Percent of m, What is the Value of 12n/m? GMAT Problem Solving
• What is the Largest Five-Digit Number which is Divisible by 17? GMAT Problem Solving
• If x is not equal to zero, and x + 1/x = 3, then what is the value of x^4 + 1/x_4? GMAT Problem Solving
• An Isosceles Right Triangle With a Leg of Length "a" And Perimeter "p" GMAT Problem Solving
• The Light In A Restroom Operates With a 15-Minute Timer GMAT Problem Solving
• Two Pipes Together Can Fill a Tank In 35 Minutes GMAT Problem Solving