CAT 2018 Slot 2 QA Question & Solution

ArithmeticMedium

A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?

$s≠6$

$s \geq 6$

$5 \leq s \leq 7$

$s \leq 6$

We can see that area of parallelogram ABCD = 2*Area of triangle ACD

48 = 2*Area of triangle ACD

Area of triangle ACD = 24

$(1/2)*CD*DA*sinADC=24$

$AD*sinADC=6$

We know that $sin\theta$ $\leq$ 1, Hence, we can say that AD $\geq$ 6

$\Rightarrow$ s $\geq$ 6