SOLUTION: PLEASE HELP ME SOLVE THESE PROBLEMS: 1. A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE? 2.IN A SOCIAL HALL OF A BUILDING, THE

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Question 227769: PLEASE HELP ME SOLVE THESE PROBLEMS:
1. A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE?
2.IN A SOCIAL HALL OF A BUILDING, THERE ARE 150 SEATS ARRANGED IN ROWS WITH 5 MORE SEATS PER ROW THAN THE NUMBER OF ROWS. HOW MANY SEATS ARE THERE IN EACH ROW?
THANK YOU!!! I REALLY APPRECIATE IT...
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Problem 1. A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE?

Step 1. The area of a rectangle A=36*16=576 (area=base*height}}}

Step 2. The square has equal sides where we let s be the side which is equal to the base and height so A=s*s=s^2.

Step 3. The areas are equal in Steps 1 and 2. Then s%5E2=576

Step 4. Take the square root to both sides of the equation or s=24.

Step 5. ANSWER: The side of the square is 24.

Problem 2. IN A SOCIAL HALL OF A BUILDING, THERE ARE 150 SEATS ARRANGED IN ROWS WITH 5 MORE SEATS PER ROW THAN THE NUMBER OF ROWS. HOW MANY SEATS ARE THERE IN EACH ROW?

Step 1. Let n be the number of rows.

Step 2. Let n+5 be the number of seats per row.

Step 3. Then, n(n+5)=150 since there are 150 seats.

Step 4. Subtract 150 to both sides of equation in Step 3.

n%5E2%2B5n-150=150%2B150

n%5E2%2B5n-150=0

Step 5. To solve, use the quadratic equation given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=5, and c=-150

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 1n%5E2%2B5n%2B-150+=+0) has the following solutons:

n%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A1%2A-150=625.

Discriminant d=625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+625+%29%29%2F2%5Ca.

n%5B1%5D+=+%28-%285%29%2Bsqrt%28+625+%29%29%2F2%5C1+=+10
n%5B2%5D+=+%28-%285%29-sqrt%28+625+%29%29%2F2%5C1+=+-15

Quadratic expression 1n%5E2%2B5n%2B-150 can be factored:
1n%5E2%2B5n%2B-150+=+1%28n-10%29%2A%28n--15%29
Again, the answer is: 10, -15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-150+%29



Selecting the positive solution of n=10 and n%2B5=15 and note the product is 150 seats.

Step 6. ANSWER: The number of seats in each row is 15 seats.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV