Question

7) A rhombus has diagonals that are 26 inches and 35inches. Which of the following is closest to the perimeter ofthe rhombus?

Answer 1

A rhombus is a parallelogram with all of its sides being equal.

The perimeter of a rhombus is given by the formula:

`P=4a`

Where

P is perimeter

a is the side length

Given two diagonal lengths of the rhombus, we can use half the length of each diagonal and the pythagorean theorem to find the side length of the rhombus.

The figure shows half the length of each diagonal and thus the half rhombus.

Using Pythagorean Theorem, we write:

`9^2+15^2=a^2`

Solving for a,

`\begin{gathered} 9^2+15^2=a^2 \\ a^2=306 \\ a=\sqrt[]{306} \\ a\approx17.49 \end{gathered}`

The perimeter would be,

`\begin{gathered} P=4a \\ P\approx4*17.49 \\ P\approx69.96 \end{gathered}`

Rounding, we can say that the perimeter is about 70 inches

Answer

(4)