Question

The two diagonals of parallelogram PQRS are 36 cm and 48 cm long. If the parallelogram is a rhombus, what is the length of side PQ?
12 cm
15 cm
30 cm
42 cm

Answer 1

i dont think its that difficult of a question so can someone please help me

Answer 2

Well, you're right, it is simple, not that difficult, but we do have the lengths of diagonals, which is pretty helpful. so take this horrible drawing of a rhombus for example. So if you look closer, you can see 4 triangles and that the diagonals bisect each other at a perpendicular line. What does that mean? Simple, it means that the angles in a perpendicular line is 90 degrees. So, the 4 triangles in the rhombus are right triangles, which means Pythagorean theorem would apply. First of all, lets get are measurements. All you need to do is divide the measurements you got, 36 and 48 and divide by 2. Because, remember, the lines were bisected, cut in two, so the measurements would be halved. You should get 24 and 18. Apply the Pythagorean theorem and you should have your answer.