Sign in
Please select an account to continue using cracku.in
↓ →
ABCD is a quadrilateral such that AD = 9 cm, BC = 13 cm and $$\angle$$DAB = $$\angle$$BCD = 90°. P and Q are two points on AB and CD respectively, such that DQ : BP = 1 : 2 and DQ is an integer. How many values can DQ take, for which the maximum possible area of the quadrilateral PBQD is 150 sq.cm?
Let $$DQ = x$$, => $$BP = 2x$$
Acc. to ques,
=> $$ar (\triangle BPD) + ar (\triangle BQD) \leq ar (PBQD)$$
=> $$(\frac{1}{2} \times AD \times BP) + (\frac{1}{2} \times BC \times QD) \leq 150$$
=> $$(\frac{1}{2} \times 9 \times 2x) + (\frac{1}{2} \times 13 \times x) \leq 150$$
=> $$31x \leq 300$$ => $$x \leq \frac{300}{31}$$
=> $$x \leq 9.68$$
Thus, for $$x$$ to be an integer and positive, 9 different values (1 to 9) are possible.
Was this solution helpful?
Click on the Email ☝️ to Watch the Video Solution
Create a FREE account and get:
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Enter OTP
Didn't receive the OTP?
Start your IIM journey with the right preparation and crack CAT 2026.
Educational materials for CAT preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
91- 6303239042
