Bunuel wrote:

What is the perimeter of a rectangle with integer sides, an area of 108 square meters and a diagonal of 15 meters?

A. 9

B. 12

C. 18

D. 42

E. It cannot be determined from the information given.

Afc0892 has posted the correct solution but I will take a different approach to explore the question in another way.

The question states that the sides are integers. So, if we assume the sides to be 'a' & 'b' then we can see two things

First

a * b = 108, in which

a &

b can take different values such as

108 * 1 = 108

54 * 2 = 108

27 * 4 = 108

18 * 6 = 108

12 * 9 = 108

Second

A right-angled triangle with hypotenuse 15 and other sides

a &

b forming a right angle between them.

Now, in a triangle, a side has to be smaller than the sum of other two sides and greater than the positive difference of other two sides.

Mathematically speaking the Hypotenuse 15 should lie between

a +

b > 15 >

a -

bIf we check from the above values, we can see that the property is satisfied only by the last two sets

That is two triangles can be made

( 18 , 6 , 15 ) and (12, 9 , 15)

Again, the hypotenuse has to be the longest side of the triangle so we can reject the first set (18, 6, 15) and land into our desired triangle (12, 9, 15)

So, sides are 12 and 9

Therefore perimeter is = 2 (12 + 9 ) = 42

this was a long story approach

The fun method is knowing Pythagorean triplets The moment you see hypotenuse as 15 and it is given that the other two sides are integers then it must fall into the category of Pythagorean triplet satisfying the base version of (3, 4, 5)

Further examples are (5, 12, 13), (8, 15, 17), (7, 24, 25)

Given that hypotenuse is 26 and other two sides are integers then they must fall into the category (5, 12, 13)

Now, you should also convince yourself that the two sides if not integers can also satisfy Pythagoras theorem. What I mean is that if it is not mentioned that the other two sides are integers then do not fit

triplet strategy un-necessarily.

Because,

12^2 + 9^2 = 15^2

Similarly,

10.198^2 + 11^2 = 15^2

It is better to visualize. I found this link

https://www.calculator.net/triangle-cal ... &x=76&y=25Hit and see different combinations of a triangle.

I know few of you may think it is all gibberish and why am I making it complex if it can be solved easily