Question

Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant nn varieties of flowers, she determines the length, LL, and the width, WW, of her garden, in feet, according to the following formulas: L(n)=n+2\qquadL(n)=n+2and \qquad W(n)=0.5n+1W(n)=0.5n+1 Let AA be the area of Kirti's flower garden if she plants nn types of flowers. Write a formula for A(n)A(n) in terms of L(n)L(n) and W(n)W(n). \qquad A(n)=A(n)= Write a formula for A(n)A(n) in terms of nn. \qquad A(n)= A(n)=

Answer 1

A(n)=0.5n^2+2n+2A(n)=0.5n

L(n)⋅W(n)

Explanation:

Answer 2

A(n) = L(n) × W(n) and
`A(n)=0.5n^(2) +2n+2`

Explanation:

We are given that the length of the rectangular garden is L and width is W.

Also, in terms of 'n',

Length is given by, L(n) = n + 2

Width is given by, W(n) = 0.5n + 1.

Now, we know that, Area of rectangle = Length × Width.

Therefore, area of Kirti's garden is given by, A(n) = L(n) × W(n).

Thus, formula of area in terms of L(n) and W(n) is A(n) = L(n) × W(n).

Moreover, as A(n) = L(n) × W(n).

i.e. A(n) = (n+2) × (0.5n+1)

i.e.
`A(n)=0.5n^(2) +n+2 * 0.5n+2`

i.e.
`A(n)=0.5n^(2) +n+n+2`

i.e.
`A(n)=0.5n^(2) +2n+2`

Hence, the formula for area in terms of 'n' is
`A(n)=0.5n^(2) +2n+2`.