MODELING WITH MATHEMATICS The football field is rectangular
(10x + 10) ft
TAR
(4x+20) ft
a. Write a polynomial that represents the area of the football field. Write your answer in standard form.
ft2
b. Find the area of the football field when the width is 160 feet.
The area is
square feet

a. area of the football field = 40ײ + 240x + 200 ft²

b. area = 57600  ft²

Step-by-step explanation:

The football field is rectangular in shape . Therefore, the area of the football field is the product of length and width.

length = 10x + 10

width = 4x + 20

area of the football field = (10x + 10)(4x + 20)

area of the football field = 40ײ + 200x + 40x + 200

area of the football field = 40ײ + 240x + 200

The standard form polynomial simply implies that the terms are ordered from the largest exponent to the smallest exponent. Therefore the standard form will be  

area of the football field = 40ײ + 240x + 200 ft²

b. area of the football field when width is 160 ft.

The width of the field = 4x + 20. Therefore

160 = 4x + 20

4x = 160 - 20

4x = 140

divide both sides by 4

x = 140/4

x = 35

area = length × width

area = (10x + 10) × 160

where

x = 35

area = (350 + 10) × 160

area = 360 × 160

area = 57600  ft²

a

step-by-step explanation: