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#1 2006-03-03 06:56:42

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What is the area of a rhombus that has one side length 10 and diagonals that differ by 4

#2 2006-03-03 07:55:41

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

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

#3 2006-03-03 08:05:48

John E. Franklin
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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.

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

#4 2006-03-03 08:21:33

MathsIsFun

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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)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman