Question

38 POINTS!!!!

The lengths of the diagonals of a rhombus are 18 cm and 24 cm. Find the perimeter and the height of the rhombus. (Hint: For the height, use the area of the rhombus as half the product of the diagonals.)

find perimeter and height

Answer 1

perimeter is 60

Explanation:

Answer 2

Hello from MrBillDoesMath!

Answer:

Perimeter = 60

Height = 18/5

Discussion:

The diagonals of a rhombus bisect each other at right angles. So a rhombus can be viewed as the union of 4 congruent right triangles, each with legs (1/2)*18 = 9 and (1/2) *24 = 12. See attachment. This gives a hypotenuse length of 15 so the Perimeter = 4 *c = 60.

The height ( = altitude) of a rhombus is

= area / length of base

= (1/2) ( (18) * 24) /c

= (1/2) ( 18 * 24) / 60

= 18/5

Thank you,

MrB