$5m*5m$

$10m*5m$

$15m*5m$

$20m*5m$

D. $20m*5m$

From the question, 2b+l = 30

=> l = 30-2b

$Area=100{m}^{2}\phantom{\rule{0ex}{0ex}}\Rightarrow l\times b=100\phantom{\rule{0ex}{0ex}}\Rightarrow b\left(30-2b\right)=100\phantom{\rule{0ex}{0ex}}{b}^{2}-15b+50=0\phantom{\rule{0ex}{0ex}}\Rightarrow \left(b-10\right)\left(b-5\right)=0$

b = 10 or b = 5

when b = 10 then l = 10

when b = 5 then l = 20

Since the garden is rectangular so we will take value of breadth 5.

So its dimensions are 20 m * 5 m