If the area ofrhombus is 48m^2 and its diagonal is 12cm . Find its altitude.
Answers
A=48 sq cm
one diagonal is 6 cm
let x and y be the two diagonals
xy=2A
6y=2*48
6y=96
y=96/6
y=16 cm for the other diagonal
the diagonals of a rhombus intersect to form right angles and also bisect each other when they intersect
draw a rhombus with the two diagonals
you have four right triangles which are all congruent
choose one, say, the one on the right side
because the diagonals bisect each other one leg of the right triangle is (1/2)(6)=3 and the other leg is
(1/2)(16)=8
the hypotenuse is a side of the rhombus
use the Pythagorean Theorem to find the hypotenuse and thus the length of a side and all sides have the same length
s^2=8^2+3^2
s^2=64+9
s^2=73
s=√73
s=8.544 cm is the length of any one of the four sides and thus the base in the formula A=bh
draw the height on the right side
A=bh
48=8.544*h
h=48/8.544
h=5.6179 cm is the height of the rhombus