SOLUTION: the diagonals of a rhombus are 10 and 24. (a) find a side of the rhombus (b) find the altitude of the rhombus

Algebra ->  Surface-area -> SOLUTION: the diagonals of a rhombus are 10 and 24. (a) find a side of the rhombus (b) find the altitude of the rhombus      Log On


   

Question 29004: the diagonals of a rhombus are 10 and 24.
(a) find a side of the rhombus
(b) find the altitude of the rhombus
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A rhombus is really an isosceles triangle plus its reflection on its base.
The diagonals meet at right angles. They bisect eachother
sides are
12%5E2+%2B+5%5E2+=+s%5E2
144+%2B+25+%2B+s%5E2
169+=+s%5E2
s+=+13
draw the figure, dropping an altitude from the 24 diagonal- call it a
[1] x%5E2+%2B+a%5E2+=+13%5E2
[2] 24%5E2+-+%2813+%2B+x%29%5E2+=+a%5E2
substitute a^2 in [2] for a^2 in [1]
x%5E2+%2B+24%5E2+-%2813+%2Bx%29%5E2+=+13%5E2
x%5E2+%2B+24%5E2+-+13%5E2+-26%2Ax+-x%5E2+=+13%5E2
cancel both x^2 and multiply both sides by -1
-24%5E2+%2B13%5E2+%2B+26%2Ax+=+-13%5E2
add +24^2 to both sides
subtract 13^2 from both sides
+26%2Ax+=+24%5E2+-+2%2A13%5E2
+26%2Ax+=+2%5E2%2A12%5E2+-+2%2A13%5E2
+13%2Ax+=+2%2A12%5E2+-+13%5E2
+13%2Ax+=+288+-+169
13%2Ax+=+119
x+=+9.15
now solve for a
a%5E2+=+13%5E2+-%289.15%29%5E2
a%5E2+=+169+-+83.72
a%5E2+=+85.27
a+=+9.23