# Integers, integers and integers? [closed]

Area of a rectangle having its length and breadth expressed as integers gets increased by 103% when its sides are increased by x% (say of length) and y% (say of breadth), where x and y are two distinct integers, greater than 0 but less than 100.

Then find the values of x and y if the measurements (of length and breadth) are integers prior to and post increment operation. Also find the numerical values of the measurements in all possible cases prior and post increment.

## closed as off-topic by boboquack, Rand al'Thor, Glorfindel, Gamow, SconibulusJul 19 '17 at 16:42

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## 1 Answer

We need to find x and y such that $(100 + x) * (100 + y) = 20300$, so let's look at a prime factorisation of $20300$:

$20300 = 2^2 * 5^2 * 7 * 29$

So we need to make two numbers from these factors, greater than $100$ but less than $200$. We can try $29 * 5 = 145$, which pairs with $2^2 * 5 * 7 = 140$, so $x = 40$ and $y = 45$ (or vice versa). Alternately, $116 * 175$ gives $x = 16$, $y = 75$.

• Yes, @Curtis J. Reubens, you got it correct ! – Mea Culpa Nay Jul 18 '17 at 13:52