Question: What is the perimeter of rectangle ABCD?

(1) Diagonal BD has length 10
(2) BDC has measure 30 degree

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: C

Solution and Explanation:
Approach Solution 1:

There is only one approach to this problem.

As per the formula, the perimeter of the rectangle ABCD is 2(AB + BC).

Statement (1) alone: Diagonal BD has length = 10 units.
As we all know that every angle in a rectangle is a right angle. Therefore, we have a right-angled triangle BDA with BD, the hypotenuse, being 10 units in length.

If BD = 10, then AB = 6 and AD = 8.
Therefore, the perimeter of rectangle = 2(6+8) = 2(14) = 28.

If BD = 10, AB = 5√2 and AD = 5√2.
Therefore, the perimeter of rectangle = 2(5√2+ 5√2 ) = 20√2.

Hence, statement (1) alone is not insufficient to get a unique value for the perimeter of the rectangle.

Statement (2) alone: ∠BDC = 30 degrees.

This implies that ∠CBD = 60 degrees since ∠BCD = 90 degrees.
This indicates that the rectangle is divided into two “30-60-90” right-angled triangles. This signifies that the sides opposite to these angles i.e. BC, CD and BD are in the ratio of 1: √3 : 2.
However, by knowing the ratio of the sides, the sides of the rectangle cannot be known.

Therefore, statement (2) alone is not sufficient to get the lengths of the sides.
Hence the perimeter of the rectangle ABCD cannot be derived.

Combining statements (1) and (2), we get:

Statement (2) tells us that the rectangle has been divided into two “30-60-90” right-angled triangles. We also derive that BC : CD : BD = 1: √3 : 2.
From statement (1) alone, we get that BD = 10 unit.

If BD = 10, BC = 5 units and CD = 5√3 units.

Since ABCD is a rectangle, CD = AB.
Therefore, perimeter of rectangle = 2(AB + BC) = 2(5√3 + 5) units.

Both statements together are sufficient to find the perimeter of the rectangle.

“What is the perimeter of rectangle ABCD”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2019”. The GMAT Quant section comprises a total of 31 questions. GMAT Data Sufficiency questions are followed by a problem statement and two factual statements. GMAT data sufficiency comes up with 15 questions which are two-fifths of the total 31 GMAT quant questions.

Suggested GMAT Data Sufficiency Samples

• Is√(x−3)2=3−x?GMAT Data Sufficiency
• What is the volume of a certain rectangular solid? GMAT Data Sufficiency
• If abc 0, is a < b < c? (1) 1/c < 1/b < 1/a (2) c > a GMAT Data Sufficiency
• A Recent Lunch Meeting at a Certain Club was Attended by Members GMAT Data Sufficiency
• w, x, y, and z are integers. If w > x > y > z > 0, is y a common GMAT Data Sufficiency
• What is the sum of 3 consecutive integers? GMAT Data Sufficiency
• Two cars A and B start from diametrically opposite points of GMAT Data Sufficiency
• What Is The Value Of X + Y In The Figure Above? GMAT Data Sufficiency
• The Length, Width, and Height of a Rectangular Box, in Centimeters are L, W, and H GMAT Data Sufficiency
• Is the perimeter of a rectangle greater than 8 inches GMAT Data Sufficiency
• Is the Positive Integer n Divisible by 8? (1) n is Divisible by the Product of Three GMAT Data Sufficiency
• Two Cars, A and B, Each Traveled a Distance of 200 Miles GMAT Data Sufficiency
• What is the SD of a Given Set of Numbers Whose Average is 5? GMAT Data Sufficiency
• Is xy > 5 GMAT Data Sufficiency
• A Hotel has Two Types of Rooms: Basic and Deluxe. On a Certain Night GMAT Data Sufficiency
• The Sequence s1, s2, s3, ..., sn, ... is Such ThatSn= 1/n − 1/n + 1 GMAT Data Sufficiency
• At The Bakery, Lew Spent A Total Of $6.00 For One Kind Of GMAT Data Sufficiency
• If p, q, x, y And z Are Different Positive Integers, Which Of The Five GMAT Data Sufficiency
• Members Of A Wrestling Team Were Weighed Twice. Was The Standard GMAT Data Sufficiency
• What Is The Number Of Female Employees In Company X ? GMAT Data Sufficiency
• If k is a Positive Integer and n = k(k + 7), is n Divisible by 6? GMAT Data Sufficiency
• In the xy Plane, What is the Slope of Line l GMAT Data Sufficiency
• The Side Of An Equilateral Triangle Has The Same Length As The Diagonal GMAT Data Sufficiency
• Each of the Students in a Certain Class Received a Single Grade of P GMAT Data Sufficiency
• Does The Graphical Representation Of The Quadratic Function GMAT Data Sufficiency
• What is the Value of m? (1) |m| = −36/m (2) 2m + 2|m| = 0 GMAT Data Sufficiency
• Do The Diagonals Of A Quadrilateral ABCD Bisect Each Other GMAT Data Sufficiency
• If X = 0.rstu, Where r, s, t, And u Each Represent A Nonzero Digit GMAT Data Sufficiency
• Is The Product Of a And b Equal To 1? GMAT Data Sufficiency
• Material A Costs $3 Per Kilogram, And Material B Costs $5 Per Kilogram GMAT Data Sufficiency
• Is the Product of a Positive and a Negative Integer Less Than -10? GMAT Data Sufficiency
• If k is not Equal to 0, 1, or -1 is 1/k>0? GMAT Data Sufficiency
• If x Is A Positive Integer, What Is The Value Of (x+24)^(½) − x^(½) GMAT Data Sufficiency
• Points x And y Lie On A Line Segment. How Many Units Long Is The Line GMAT Data Sufficiency
• Which Sport Utility Vehicle has a Higher List Price, the Touristo or GMAT Data Sufficiency
• What is The Average (arithmetic mean) Annual Salary of the 6 Employees GMAT Data Sufficiency
• If S is a Set of Ten Consecutive Integers, is the Integer 5 GMAT Data Sufficiency
• What is the Perimeter of a Square Chessboard, If a Chessboard is made GMAT Data Sufficiency
• Is the sum of four different positive prime integers an odd integer? GMAT Data Sufficiency
• Is Positive Integer x Divisible By 24? GMAT Data Sufficiency
• 10 Students took a Chemistry Exam that was Graded on a Dcale of 0 to 100 GMAT Data Sufficiency
• If m and n are positive integers, is the remainder of GMAT Data Sufficiency
• In quadrilateral ABCD, is AC longer than BD GMAT Data Sufficiency
• N is a positive integer. Is n the square of an integer? GMAT Data Sufficiency
• If z Is An Integer Smaller Than Integer n But Greater Than Zero GMAT Data Sufficiency
• If y Is An Odd Number And x^3 ∗ y^4 = 648, y=? 1) y Is Positive 2) x Is Gmat Data Sufficiency
• A Pyramid-Shaped Box To Protect A Plant Is Constructed With 4 Lateral Faces GMAT Data Sufficiency
• Is abc/d an Integer if a, b, c, and d are Positive integers? GMAT Data Sufficiency
• If n is a positive integer, is (1/10)^n < 0.01? GMAT Data Sufficiency
• If m and n are nonzero integers, is m^n an integer? GMAT Data Sufficiency