Question

you are growing zucchini plants in your garden. in the figure, the entire garden is rectangle qrst. each unit in the
q(1, 13)
r(7, 13)
u(1, 4) v(4, 4)
t(1, 1) w(4, 1) s(7, 1)
a. find the area of the garden.
a = □ ft²
b. zucchini plants require 9 square feet around each plant. how many zucchini plants can you plant?
you can plant □ zucchini plants

Explanation:

Step1: Calculate length of rectangle

Use the distance formula for points on a horizontal or vertical line. For the length of the rectangle \(QS\) (where \(Q(1,13)\) and \(S(7,1)\)), since the \(x - \)coordinates are used for the horizontal length. The length \(l\) between \(Q(1,13)\) and \(R(7,13)\) (or \(T(1,1)\) and \(S(7,1)\)) is \(l=\vert7 - 1\vert=6\).

Step2: Calculate width of rectangle

For the width of the rectangle, using the \(y - \)coordinates of \(Q(1,13)\) and \(T(1,1)\). The width \(w=\vert13 - 1\vert = 12\).

Step3: Calculate area of rectangle

The area formula of a rectangle is \(A=l\times w\). Substitute \(l = 6\) and \(w = 12\) into the formula, so \(A=6\times12 = 72\) square - feet.

Step4: Calculate number of plants

If each zucchini plant requires 9 square - feet, then the number of plants \(n=\frac{A}{9}\). Substitute \(A = 72\) into the formula, \(n=\frac{72}{9}=8\).

Answer:

a. \(72\)
b. \(8\)