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A rhombus has sides of length 10, and its diagonals differ by 4. What is its area?

 May 4, 2020
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rhombus is made of 4 right triangles with the same area
so using pythagorean theorem on one of the 4:
the sides of the triangle would be d/2 and (d+4)/2 and hypotenuse 10
(d/2)^2 + ((d+4)/2)^2 = 10^2 (solve for d)
1/4 * d^2 + 1/4 * (d+4)^2 = 100
d^2 + (d+4)^2 = 400 (multiplied both sides by 4)
d^2 + d^2 + 8d + 16 = 400
2 * d^2 + 8d + 16 = 400

d^2 + 4d + 8 = 200 (divided both sides by 2)
d^2 + 4d - 192 = 0 (16*12=192)
(d + 16)(d - 12) = 0 (2 answers use the positive one)
d = 12 inches
so d+4 = 16 inches
now we got measure of both diagonals
Area = 1/2 times the product of the diagonals
Area = 1/2 * 12 * 16
Area = 1/2 * 192
Area = 96 inches^2

 May 4, 2020

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