SOLUTION: urgent!!!!solve this problem............ by application(algebra for 2nd year) 1.the product of two consecutive integers is 240.Find the two integers. 2.find the length and width

Question 12949: urgent!!!!solve this problem............
by application(algebra for 2nd year)
1.the product of two consecutive integers is 240.Find the two integers.
2.find the length and width of a rectangle whose area and perimeter are 51 sq.m. and 40 m.,respectively.
I need it right now plsasssss!!!!!!!!!!!!!!!
clear the steps in solving it............
Answer by askmemath(368) (Show Source): You can put this solution on YOUR website!
Since they are consecutive numbers, one number is bigger than the other by 1.
So if 1 number is X the other number is X+1
Product = X(X+1)= 240
Do you know how to find the factors of 240?
take a graph paper: x x y = 240
but x and y are very close to being equal which means the figure having area 240 is close to being a square and 15 square is close to the answer 240
And 240 has 0 in the final place
So it�s either 15x16 or 19x20
Verifying 15x16 = 240
2.) Area = lxb = 51
perimeter = 2(l+b) = 40
l+b = 20
By observation you will see that 52 has 2 factors 3 and 17 both of which are Prime numbers.
So length and breadth = 17 and 3
The other way of doing this is as follows
Find l-b
l-b = Square root of (l+b)^2 -4lb
= Sq Root (400 - 4x51)
= Sq Root( 196)
l-b = 14
l+b = 20
Adding
2l = 34
l =17
Hence b = 3
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