Question 134085: Hi ,
I was hoping you could help me with two more question. I have tried to find a formula but I can't and I'm wasting too much time. My class is tomorrow evening.
1. Determine two numbers whose sum is 15 and the sum of its square roots is 137. I know the answer is 11 and 4 but what formula do I use.
7. The perimeter of a rectangle is 20 inches and its area is 24 inches squared. Determine the lengths of its sides. I know that the sides are 6" and 4" but I need to show my work. I just used logic to find the numbers.
8. The perimeter of a rectangle es 24cm and its area is 32 cm squared. Find the lengths of its sides. Again I know that the answer is 8cm and 4cm but what is the formula?
I really appreciate the help
Thanks,
Anne
Found 2 solutions by solver91311, Ganesha:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! In the first place, you have a problem with the way you stated question number 1. If two numbers have a sum of 15, they can't have a sum of their square ROOTS be a larger number, and certainly not 137. Since you gave the answers as 11 and 4, then the question must have read: '...the sum of their squares is 137.'
Presuming that to be true, here's how to solve it.
First number: 
Second number: 
Square of the first number: 
Square of the second number: 
Sum of the numbers: 
Sum of the squares: 
We are given:
Solve the first equation for either of the variables:
Substitute this value into the second equation:
Expand and simplify:
The lead coefficient is an integer factor of all the coefficients, so divide:
Factor the trinomial:
 and  , so:
 , so:
 or 
Check the answer:
=================================
Perimeter = 
Area = 
Solve the perimeter equation for either variable:
Substitute in the Area equation:
Factor:
 or 
Traditionally, the width is shorter than the length, so the width is 4, so  => =>
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Do problem #8 the same way I just showed you for problem #7
Answer by Ganesha(13)  (Show Source):
You can put this solution on YOUR website! 1
x+y=15 (1)and x^2+y^2 =137
x+y)^2 = 15^=225. 2xy = 225-137= 88
x-y)^2 =137-88 = 49, Hence
x-y=7 (2). from (1) and (2) 2x=22 x=11 2y=8 y=4
The other 2 are similar please do it similarly.
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