SOLUTION: The area in square units of a rhombus for which one side has length 10 units and the diagonals differ by 4 units is A 27 b 49 c 64 d 88 e 96

Question 281415: The area in square units of a rhombus for which one side has length 10 units and the diagonals differ by 4 units is
A 27 b 49 c 64 d 88 e 96
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
The diagonals of a rhombus are always perpendicular.
Let the base of each of the 4 right triangles be x and the altitude be x+2 (not x+4 because we are using 1/2 the diagonals).
x^2+(x+2)^2=100 Pythagoras
x^2+x^2+4x+4-100=0
2x^2+4x-96=0
x^2+2x-48=0
(x+8)(x-6)=0
x=6
A=.5ab
=.5*6*8
=24 (1/4 area of the rhombus)
24*4=96 sq units
.
Ed
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