Question

The perimeter of rectangle A is 200 meters. The length of rectangle B is 10 meters less than the length of rectangle A and the width of rectangle B is 10 meters more than the width of rectangle A. If rectangle B is a square, what is the width, in meters, of rectangle A? [Official GMAT-2018]

Hint:

For rectangles, the perimeter is calculated as \( 2 \times (\text{Length} + \text{Width}) \). For square conditions, equate length and width.

Answer 1

Step 1: Define the variables.
Let the length of rectangle A be \( X \) meters and the width of rectangle A be \( Y \) meters.
Step 2: Perimeter condition for rectangle A.
The perimeter of rectangle A is given by: \[ 2(X + Y) = 200 \quad \Rightarrow \quad X + Y = 100 \quad \text{(Equation 1)} \] Step 3: Rectangle B's conditions.
For rectangle B, the length is \( (X - 10) \) meters and the width is \( (Y + 10) \) meters. Since rectangle B is a square, we know: \[ X - 10 = Y + 10 \quad \Rightarrow \quad X - Y = 20 \quad \text{(Equation 2)} \] Step 4: Solve the system of equations.
Add equations (1) and (2): \[ (X + Y) + (X - Y) = 100 + 20 \quad \Rightarrow \quad 2X = 120 \quad \Rightarrow \quad X = 60 \] Step 5: Find \( Y \).
Substitute \( X = 60 \) into equation (1): \[ 60 + Y = 100 \quad \Rightarrow \quad Y = 40 \] Step 6: Conclusion.
The width of rectangle A is \( Y = 40 \) meters. Therefore, the correct answer is (2) 40 meters.