The diagonals of a rhombus measure 10cm and 24cm. Find its perimeter.
Since they right-bisect each other, you will have 4 congruent right-angled triangles, with legs of 5 and 12. Perhaps you recognize the 5-12-13 right-angled triangle, if not use Pythagoras to find the hypotenuse to be 13
So the perimeter is ......
To find the perimeter of a rhombus, we need to know the length of its sides.
First, let's understand some properties of a rhombus.
A rhombus is a quadrilateral with all four sides of equal length. Additionally, its diagonals bisect each other at a right angle.
In our case, we are given the lengths of the diagonals. Let's call the length of one diagonal "d1" and the length of the other diagonal "d2".
Given that d1 = 10cm and d2 = 24cm, we can use these diagonals to find the length of the sides of the rhombus.
To do this, we can use the property of a rhombus that states the product of the diagonals is equal to the product of the sides.
So, we have d1 * d2 = side length * side length
Plugging in the given values, we get 10cm * 24cm = side length * side length
240cm² = side length²
Taking the square root of both sides, we have √240cm² = side length
Therefore, the length of each side of the rhombus is approximately 15.49cm (rounded to two decimal places).
Now we can calculate the perimeter by adding up all four sides: perimeter = 4 * side length.
Plugging in the value of the side length (15.49cm), we get: perimeter = 4 * 15.49cm.
Finally, we can calculate the perimeter of the rhombus:
perimeter = 4 * 15.49cm = 61.96cm.
Therefore, the perimeter of the rhombus is approximately 61.96cm (rounded to two decimal places).