SOLUTION: the sides of a rhombus are 5 cm each and one diagonal is 8 cm. calculate the length of the other diagonal and the area of the rhombus.

Algebra ->  Polygons -> SOLUTION: the sides of a rhombus are 5 cm each and one diagonal is 8 cm. calculate the length of the other diagonal and the area of the rhombus.      Log On


   

Question 941901: the sides of a rhombus are 5 cm each and one diagonal is 8 cm. calculate the length of the other diagonal and the area of the rhombus.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The two diagonals divide the rhombus into 4 congruent right triangles:

The Pythagorean theorem, applied to the triangle with the measures shown, states that
x%5E2%2B%284cm%29%5E2=%285cm%29%5E2 .
You can solve for {{x}}} to find that x=3cm .
That is half of the other diagonal, so the other diagonal measures
2%2A%283cm%29=highlight%286cm%29 .

The area of the rhombus is half the area of the large rectangle around it,
%286cm%29%2A%288cm%29%2F2=highlight%2824%29cm%5E2 .