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

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) (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

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

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.

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

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

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=625 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10, -15. Here's your graph:

Selecting the positive solution of and 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

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