Among all the parallelograms whose diagonals are 10 and 4,the one… - Vidyadip

MCQ

Among all the parallelograms whose diagonals are $10$ and $4$,the one having maximum area has its perimeter lying in the interval

A
$(19,20]$
B
$(20,21]$
✓
$(21,22]$
D
$(22,23]$

✓

Answer

Correct option: C.

$(21,22]$

c
(c)

Area of parallelogram whose diagonals are 10 and 4 and if angle between adjacent side is $\theta$ is

$A=\frac{10 \times 4}{\sin \theta}$

The area will be maximum if $\theta=\frac{\pi}{2}$, so the parallelogram must be rhombus

Perimeter of rhombus

$=4 \sqrt{2} \overline{9}=\sqrt{46} \overline{4} \text { and } \sqrt{46} \overline{4} \in(21,22]$

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