Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 152428This question is from textbook elementary and intermediate algebra concecpts and applications
: Can someone please refresh my memory? I really need it Thanks


Solve the following problems involving applications of polynomials.
a. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
b. A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
c. Three consecutive odd integers are such that the square of the third is 264 more than the square of the second. Find the three integers.

This question is from textbook elementary and intermediate algebra concecpts and applications
: Can someone please refresh my memory? I really need it Thanks


Solve the following problems involving applications of polynomials.
a. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
b. A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
c. Three consecutive odd integers are such that the square of the third is 264 more than the square of the second. Find the three integers.


Answer by jojo14344(883) About Me  (Show Source):
You can put this solution on YOUR website!
a.) Same as GEOMETRY PROBLEM #151709
SEE ANSWER# 111525 -------> DONE.
b.)The Length=L is 100ft longer than the width=W --->L=W+100ft
The diagonal=D side given = 500ft, by PYTHAGOREAN THEOREM:
D^2=L^2+W^2, but L=W+100ft, so
D^2=(W+100)^2+W^2
500^2=W^2+200W+10000+W^2
0=2W^2+200W+10000-250000 ---> 2W^2+200W-240000=0, Divide the whole eqn by 2:
cross(2)W+cross(200)100W-cross(240000)120000=0(1/cross(2))
W+100W-120000=0 ---> a=1,b=100, & c=-120000
By Pyth. theorem:
w=(-b+-sqrt(b^2-4ac))/(2a)
w=(-100sqrt(100^2-4*1*(-120000)))/(2*1)
w=(-100+-sqrt(10000+480000))/2
w=(-100+-sqrt(490000))/2 ------> w=(-100+-700)/2
2 values:
w=(-100+700)/2=600/2=300ft ----------> TO BE USED ----> WIDTH=300ft
w=(-100-700)/2=-800/2=-400ft --------> DO NOT USE
So, L=300+100=400ft
To check, go back PYTH Theorem: 500^2=400^2+300^2=160000+9000
25000=25000, good!
.
3.) Let X = 1st odd integer
X+2= 2nd odd integer
X+4= 3rd integer
condition: square of 3rd is 264 more than suqrae of 2nd: to show,
(x+4)^2=264+(x+2)^2
cross(x^2)+8x+16=264+cross(x^2)+4x+4
8x-4x=264+4-16 --> cross(4)x/cross(4)=cross(252)63/cross(4)
x=63 -----------------------> 1st odd integer
63+2=65 --------------------> 2nd odd integer
63+4=67 --------------------> 3rd odd integer
in doubt? go back to the condition:
(67^2)=264+(65^2)
4489=264+4225
4489=4489
Thank you,
Jojo