Question

The lengths of the diagonals of a rhombus are 18 and 24

Answer 1

The length of each of the sides of the rhombus is 15.

This question is incomplete, the complete question is:

The length of the diagonals of a rhombus are 18 and 24. Find the length of each side of the rhombus

Given the data in the question;

• Diagonal 1 of the rhombus; $p = 18$

• Diagonal 2 of the rhombus; $q = 24$

• Length of each side of the rhombus; $a = \ ?$

Rhombus

A Rhombus is simply a quadrilateral whose four sides are all equal in   length i.e its an equilateral quadrilateral.

Now, to determine the length of each sides of the rhombus, we create ab expression from Pythagoras theorem:

$a = \frac{\sqrt{p^2+q^2} }{2}$

Where a is the length of the sides and pq are the diagonals.

We substitute our given values into the expression above.

$a = \frac{\sqrt{p^2 + q^2} }{2} \\\\a = \frac{\sqrt{18^2 + 24^2} }{2}\\ \\a = \frac{\sqrt{324 + 576} }{2}\\ \\a = \frac{\sqrt{900} }{2}\\ \\a = \frac{30}{2}\\ \\a = 15$

Therefore, the length of each of the sides of the rhombus is 15.

Learn more about rhombus: https://brainly.com/question/14462098