Question

what expression in terms of n can be used to represent ad in rhombus abcd? a b 4n - 3 2n + 5 d c a. (2n + 5)^2+(4n - 3)^2 b. 2(2n + 5)+2(4n - 3) c. √((2n + 5)+(4n - 3)) d. √((2n + 5)^2+(4n - 3)^2)

Explanation:

Step1: Recall property of rhombus

In a rhombus, the diagonals are perpendicular bisectors of each other. Let the diagonals of rhombus \(ABCD\) intersect at a point. The lengths along the diagonals are \(4n - 3\) and \(2n+5\).

Step2: Apply Pythagorean theorem

If we consider half - lengths of the diagonals of the rhombus, and we want to find the side length \(AD\) of the rhombus. By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the side of the rhombus and \(a\) and \(b\) are half - lengths of the diagonals. Here, if we consider the right - triangle formed by the half - diagonals, the side length \(AD\) of the rhombus is given by \(AD=\sqrt{(2n + 5)^{2}+(4n-3)^{2}}\)

Answer:

D. \(\sqrt{(2n + 5)^{2}+(4n - 3)^{2}}\)