The height of a rhombus is 4.1 centimeters. Its base length is 6.6 centimeters and the length of one of its diagonals is 4.3 centimeters. Find to the nearest tenth the length of the other diagonal.
So we’re working with a rhombus and we want to find the length of the other diagonal. Usually when solving an equation like this, we’re given the area and we are trying to find some measurement. But in this case, we don’t know the area. However, we’re given many different lengths. We know that the height is equal to 4.1 centimeters, the base length is equal to 6.6 centimeters, one of its diagonals is 4.3 centimeters, and we’re asked to find the length of the other diagonal.
So let’s look at some formulas that we know about a rhombus. The area of a rhombus is equal to the height times the base length or we can also solve for the area by taking one-half times diagonal number one times diagonal number two. So let’s go ahead and find the area of the rhombus using the height times the base length. The height was equal to 4.1 centimeters and the base length was equal to 6.6 centimeters. So if we multiply these together, we get 27.06 square centimeters.
So now, we can take our other formula and set it equal to the area because we’ve already solved for it. And we can also plug in the length of diagonal number one, which was equal to 4.3 centimeters. So 4.3 centimeters times one-half is equal to 2.15 centimeters.
So now, to solve for diagonal number two, let’s go ahead and divide both sides of the equation by 2.15 centimeters. They cancel on the right and we find that diagonal number two is equal to 12.586 centimeters. However, we’re supposed to round to the nearest tenth. So we either need to keep this five a five or round it up to a six. We’ll look at the number to the right of it. And since eight is five or larger, we will round the five up to a six.
Therefore, the length of the other diagonal would be 12.6 centimeters.