Question

In a garden, roses and marigolds are planted in squares plots. The length of the square plot in which marigolds are planted is 6 meters greater than the length of the square plot in which roses are planted. If the perimeter of the square plot of roses is 64 meters then, how much bigger is the area of marigold plot than the rose plot?

• A. 200 metres square
• B. 225 metres square
• C. 228 metres square
• D. 235 metres square

Answer 1

The correct option is C 228 metres square

Let the length of the side of the rose plot = $x$ metres,
the length of the side of the marigold plot = $(x+6)$ metres,

Area of the rose plot = $x^2$ metres square,
Area of the marigold plot = $(x+6{)}^2$ metres square,
Perimeter of the square plot of rose plot$=4x$ metres
$4x=64,$
$x=16\text{metres.}$
The difference between areas of marigold plots and rose plots is
$=(x+6{)}^2-x^2$
$=x^2+36+12x-x^2$
$=36+12x=36+12\left(16\right)=228$ metres square.