Question

In this activity, you will apply mathematics to problems arising in everyday life and communicate mathematical ideasusing multiple representations.Part AMelissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of thegarden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed thewidth of the tomato patch by 5 feet.Let x represent the length, in feet, of the square tomato patch.Question 1QuestionWrite expressions to represent the length and width of Melissa's vegetable garden in terms of x.Enter the correct answer in the box.

Answer 1

The vegetable garden is rectangular.

In it are tomato square patches

Given:

x = length of the tomato square patch

Since it is a square patch, the width of the tomato patch is also the length.

Hence, x = width of the tomato square patch

Also,

A = rectangular vegetable garden

B = tomato square patch

l = length of the vegetable garden

w = width of the vegetable garden

The expressions that represent the length and width of Melissa's vegetable garden is shown mathematically below;

$\begin{gathered} \text{She wants the length of the garden to exc}eed\text{ thre}e\text{ times the length of the tomato patch by 2 f}eet. \\ l-3x=2 \\ l=3x+2 \end{gathered}$$\begin{gathered} \text{Also, she wants the garden's width to exc}eed\text{ the width of the tomato patch by 5 f}eet \\ \text{The length and width of the tomato patch are the same since it is a square patch. Hence, the width of the tomato patch is x} \\ w-x=5 \\ w=x+5 \end{gathered}$

Therefore, the length and width of Melissa's vegetable garden in terms of x is given by;

$\begin{gathered} l=3x+2 \\ w=x+5 \end{gathered}$