SOLUTION: I have this Maths Question. The sides of a rectangle are in the ratio 2:3 The diagonal is of length 26cm. You have to find the perimeter of the rectangle. I know that

Algebra ->  Pythagorean-theorem -> SOLUTION: I have this Maths Question. The sides of a rectangle are in the ratio 2:3 The diagonal is of length 26cm. You have to find the perimeter of the rectangle. I know that      Log On


   

Question 330574: I have this Maths Question.
The sides of a rectangle are in the ratio 2:3
The diagonal is of length 26cm.
You have to find the perimeter of the rectangle.
I know that one side is two parts of the ratio and the other side is three parts of the ratio.
I have squared 26² To get 676.
Using Pythagoras theorem. The square of the sides with ratio 2: and 3: equal the longest side which is 26cm squared 676.
I tried taking the ratio’s dividing it 676 by 5, but this does not give the correct lengths for each side.
The answer for the whole perimeter is 20√13
From the answer I worked out from the ratio that the rectangle is made up of sides length 4√13, 6√13, 4√13, 6√13, adding these surds together gives you the answer 20√13.
4√13 = √16 * √13 = 208
6√13 = √36 * √13 = 468
208 + 468 = 676
What I can’t do is work out from the diagonal side 26cm squared to 676, how you then split the numbers into their correct ratio’s
I backward worked it out after looking at the answer but don’t know the procedure to do this.
Any help would be gratefully received.
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
I read your post twice and cannot follow exactly what it is you're asking.
The ratio given is 2:3 for the sides, which becomes 2x:3x.
We use the Pythegorean Theorem to find x.
(2x)^2 + (3x)^2 = 26^2
4x^2 + 9x^2 = 676
13x^2 = 676
x^2 = 676/13
x^2 = 52
x = sqrt[52]
NOTE: sqrt = square root for short.
The perimeter of a rectangle is found using P = 2L + 2W.
P = 2(sqrt[52]) + 2(sqrt[52])
P = 4(sqrt[52]).
I hope this helps a bit.