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

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step-by-step explanation: ; )

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.