Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by two feet. She also wants the garden’s width to exceed the width of the tomato patch by five feet. Part A
Melissa wants to know how the width and length of the garden relate to the length of the square tomato patch. If each side of the tomato patch is x feet, write the functions WG(x) and LG(x) to represent the garden’s width and length, respectively.

Part B
Write the function AG(x) representing the area of the garden in terms of x.

Part C
If the sides of the square tomato patch are seven feet, find the area of the garden.

Part D
Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. She wants its width to be half the width of the tomato patch, and its length must exceed the length of the tomato patch by two feet. Write the functions WB(x) and LB(x) representing the width and length, respectively, of the bell pepper patch.

Part E
Write the function AB(x) representing the area of the bell pepper patch in terms of x.

Part F
Write the function ATB(x) representing the combined area of the tomato patch and the bell pepper patch.

Part G
You’ve written functions to represent the area of the tomato patch and the area of the bell pepper patch. Now write the function AR(x) for the remaining planting area in the garden.

Part H
If Melissa wants the area of the bell pepper patch to be 31.5 square feet, find the area of the remaining space in the garden after planting tomatoes and bell peppers.