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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

Hello from MrBillDoesMath!

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