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MathsIsFun
2006-03-03 08:21:33

Yes! The diagonals of a rhombus are at right angles.

So imagine a triangle whose base is the base of the rhombus, but whose apex is the middle, then use Pythagoras Theorem

a2 + b2 = c2

Remember, these are going to be half-diagonals, so the difference will only be 2, and lets call the short diagonal "x":

x2 + (x+2)2 = 102

x2 + x2 + 4x + 22 = 102

2x2  + 4x + 4 = 100

2x2  + 4x -96 = 0

This is a Quadratic Equation and the solutions are 6 and -8. The lengths won't be negative so "6" is the answer.

That is the short "half-diagonal", so the full diagonal will be 12, and the longer diagonal 16.

The area will be ½ × 12 × 16 = 96 (because you can calculate the area of a rhombus by multiplying the diagonals and then halving)

John E. Franklin
2006-03-03 08:05:48

Draw the slanted square (rhombus), draw the diagonals so now you have a
picture of kite without the tail flying in the wind.
Notice the right triangles.
Assign values like x and x-2 and 10 and apply pythagoreans theorm
Then the area is four right triangles, or two rectangles, if you pair up
the right triangles by sliding them all around.

John E. Franklin
2006-03-03 07:55:41

Well a rhombus has all four sides the same length and is a special parallelogram,
so all sides are 10.  Hope that helps you.