If the perimeter of a rectangle is 75 meters, and the length is 1.5 times the width, find the area of the rectangle in square meters. Round your answer to two decimal places.

A) 937.50 square meters
B) 8.66 square meters
C) 225.00 square meters
D) 527.34 square meters
E) 337.50 square meters

The perimeter of a rectangle is given by the formula $2l+2w=P$ , where $l$ is the length, $w$ is the width, and $P$ is the perimeter. Given that the length is 1.5 times the width ( $l=1.5w$ ) and the perimeter is 75 meters, we can set up the equation $2(1.5w)+2w=75$ . Simplifying, we get $3w+2w=75$ , which leads to $5w=75$ , so $w=15$ meters. The length $l=1.5w=22.5$ meters. The area of a rectangle is given by $A=lw$ , so the area is $15\times 22.5=337.50$ square meters.