Please check for me and tell me how to correct, thank you.
Mary wants to put a walk( 10 ft wide)all the way around her house. house Length=60 ft width 45 ft
A. write a polynomial that represents the total area of the house and walk
total area of walk and house =
(2x+60)(2x+45
= 4x^2 + 90x + 120X + 2700
= 4x^2 + 210x + 2700
b. Find the combined area of house/walk.
X= 10 width of walk
Area = 4(10)^2 + 210(10) + 2700
= 4(100) + 2100 + 2700
=400 + 2100 + 2700
= 5200 sq ft
To correct your solution:
A. To represent the total area of the house and walk, you correctly use the expression (2x + 60)(2x + 45). However, you made an error in expanding it.
Expanding (2x + 60)(2x + 45), you should multiply each term in the first parentheses by each term in the second parentheses:
(2x + 60)(2x + 45) = 2x * (2x + 45) + 60 * (2x + 45)
= 2x * 2x + 2x * 45 + 60 * 2x + 60 * 45
= 4x^2 + 90x + 120x + 2700
= 4x^2 + 210x + 2700
So the corrected polynomial representation of the total area of the house and walk is 4x^2 + 210x + 2700.
B. To find the combined area of the house and walk, you need to replace "X" with the width of the walk, which is correctly given as 10. However, you made an error in the calculation.
Calculating the area with X = 10:
Area = 4(10)^2 + 210(10) + 2700
= 4(100) + 2100 + 2700
= 400 + 2100 + 2700
= 5200 sq ft
So the corrected combined area of the house and walk is 5200 sq ft.