# A woman has two rectangular gardens. The larger garden is five times as wide and three times as long as the smaller one. If the area of the smaller one is x, what is the difference in size of the two gardens?

Mar 23, 2017

Let the length and breadth of smaller rectangular garden be $l \mathmr{and} b$ respectively.

So the length and breadth of larger rectangular garden will be $3 l \mathmr{and} 5 b$ respectively.

Area of smaller garden $l \times b = x$

And area of larger one will be

$= 3 l \times 5 b = 15 l \times b = 15 x$

So difference in size will be
$= 15 x - x = 14 x$

Mar 23, 2017

The difference in size of the two gardens is $14 x$.

#### Explanation:

The smaller garden $= {x}^{2}$

width of the bigger garden $= x + x + x + x + x = 5 x$

length of the bigger garden $= x + x + x = 3 x$

Area of the bigger garden$= 3 x \times 5 x = 15 {x}^{2}$

The area of the smaller garden$= {x}^{2}$

$\therefore \frac{15 {x}^{2}}{x} ^ 2 = 15$

$\therefore$ the bigger garden is 15 times bigger than the smaller garden.

Hence, if the area of the smaller one is $x$, area of the bigger one is $15 x$ and difference in size of two gardens is $15 x - x = 14 x$

Area of a rectangle: example: $a \times a = {a}^{2}$ so the area
can't be just 15x,it must be $15 {x}^{2}$

same with the smaller garden$= {x}^{2}$

If you make a sketch of the bigger garden and you
mark off 3 points on two sides and 5 points on the
other two sides and join the points,you get 15 sections.
I think the x should have been ${x}^{2}$ we talk about areas.