Video Transcript
In the rhombus 𝐴𝐵𝐶𝐷, the side
length is 8.5 centimeters and the diagonal lengths are 13 centimeters and 11
centimeters. Find the length of 𝐷𝐹. Round your answer to the nearest
tenth.
We have two formulas for the area
of a rhombus. The first tells us that the area is
equal to half the product of the diagonals. Let’s substitute in the diagonal
lengths that we have been given. 11 times 13 divided by two equals
71.5 square centimeters. The second rhombus area formula
tells us that the area of the rhombus is equal to its side length times its
perpendicular height. The perpendicular height of this
rhombus is 𝐷𝐹, which is equal to 𝐷𝐸, because triangles 𝐷𝐶𝐸 and 𝐴𝐷𝐹 are
congruent. Substituting in the side length of
8.5 and the area of 71.5 that we have just calculated, we have 71.5 equals 8.5 times
𝐷𝐹. Rearranging, we find that the
length of 𝐷𝐹 is 71.5 divided by 8.5, which is 8.4 centimeters to the nearest
tenth.
