Answer:
Option C
Explanation:
Given : |a|=$2 \sqrt{2}$,|b|=3
One diagonal is 5a+2b+a-3b=6a-b
Length of one diagonal
=|6a-b|
=$\sqrt{36a^{2}+b^{2}-2 \times 6|a|.|b| \cos 45^{0}}$
=$\sqrt{36\times 8+9-12\times2\sqrt{2}\times3\times\frac{1}{\sqrt{2}}}$
=$\sqrt{288+9-12\times6}=\sqrt{225}=15$
other diagonal is (5a+2b)-(a-3b)=4a+5b
Its length is
=$\sqrt{(4a)^{2}+(5b)^{2}+2\times |4a||5b| \cos 45^{0}}$
=$\sqrt{16\times8+25\times9+40\times6}=\sqrt{593}$
