Question

A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. What is the length of this garden?

Answer 1

Length of garden is `14`

Explanation:

Let the length be `L` cm. and as area is `140` cm., it being a product of length and width, width should be `140/L`.

Hence, perimeter is `2xx(L+140/L)`, but as perimeter is `48`, we have

`2(L+140/L)=48` or `L+140/L=48/2=24`

Hence multiplying each term by `L`, we get

`L^2+140=24L` or `L^2-24L+140=0` or

`L^2-14L-10L+140=0` or

`L(L-14)-10(L-14)=0` or

`(L-14)(L-10)=0`

i.e. `L=14` or `10`.

Hence, dimensions of garden are `14` and `10` and length is more than width, it is `14`

Answer 2

The garden has sides of 14cm and 10cm. Length is 14cm.

Explanation:

We know that it is a rectangle, so each pair of opposite sides are the same length. We denote one set of sides length `x` and the other set length `y`.

Therefore, the perimeter is given by `2x+2y`.

`therefore 2x + 2y = 48cm`

The area of a rectangle is given by the product of it's length and breadth, ie

`A = xy = 140cm^2`

`implies x = 140/y`

`2(140/y) + 2y = 48`

`280/y + 2y = 48`

`140 + y^2 = 24y`

`y^2-24y + 140 = 0`

Use quadratic formula:

`y=(24+-sqrt(24^2-4(1)(140)))/2 = (24+-sqrt(16))/2 = 10 or 14`

`y=10 implies x = 14`

`y = 14 implies x = 10`