a and b are the diagonals of the rhombus. Heres the second part of my question: "The perimeter of a rhombus is 80cm. The lengths of its diagonals are in the ration 3:4. what is the length of each diagonal." ok so i'm pretty sure this has to do with the pythagorean theorem, but i keep getting stuck.
2007-03-11 10:49:11 · 1 answers · asked by horsefreakmillie 2 in Science & Mathematics ➔ Mathematics
The thing to notice is that the diagonals of a rhombus are perpendicular to each other. That gives you four identical right triangles. The two legs of those triangles have length a/2 and b/2. Therefore, the hypotenuse of these triangles is √((a/2)²+(b/2)²) = (√(a²+b²))/2. Since the perimiter is made up of the four hypotenuses, just multiply by 4: Perimiter = 2√(a²+b²)
If you have understood this, part b will be easy because you just have to write 3a = 4b, isolate either a or b (bring everything over to the other side) and then plug it into the above formula.
2007-03-11 11:00:11 · answer #1 · answered by Quadrillerator 5 · 1⤊ 0⤋