00:01
In the given question we are told that the lengths of diagonals of a parallelogram are ac which is 26 or 28 it is 28 centimeters and bd is 24 centimeters so if we are drawing a parallelogram like this let's say it is named a b b b, c and d.
00:32
We are told the diagonal ac is having a length of 28.
00:42
So since ac is the bigger diagonal, let's draw this like this, just label it the other way around.
00:51
That is a, b, c and d.
00:55
Now we are told ac is 28.
00:59
Units of length and bd bd is 24 centimeters ac is 28 centimeters and bd is 24 centimeters and we are told that the angles intersect at an angle of 43 degrees so this angle is 43 degrees we could say this is this angle is also 43 degrees and and these two angles would be of the same measure as well which we can write later but now what we are told to find is the length of the sides of the parallelogram so we are given a hint in the problem that the diagonals of a parallelogram bisect one another so what we could do over here is first let's take this this let's take let's look at this parallelogram we can see that let's say this point over here is o in the triangle a o b the triangle a o b a o is 28 divided by 2 let's write the hint over here that is the diagonals of a parallelogram bisect each other which means they cut each diagonals cut themselves in half so this means that a o is half of ac that is 28 divided by 2 which is 14 centimeters and similarly for b o it is half of bd so it is 12 centimeters meters and now we know that the angle over here is 43 degrees since the this angle is obviously an obtuse angle right so this angle these are the angles that we are being told is to be is to have a measure of 43 degrees now what we are going to what we have to find is the length of the side a b of the parallelogram and we are going to solve this triangle in order to find the side a, b, which would be the side of the parallelogram also.
03:34
So a low we are going to use over here is the low of cosines.
03:38
And according to the low of cosines, what it says is that if we have a triangle in which we know the two sides of the, the length of two sides of the triangle is known as a and b, and an included angle is also known...