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# help

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Problem:

A rhombus with area 840 has a diagonal of length 40 . What is its side length?

Apr 21, 2019

#1
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We have $$\frac{pq}{2}$$, as $$p$$ and $$q$$ are the two diagonals. Thus, we have $$\frac{40*q}{2}=840$$, and $$40q=1680, q=42.$$

Now, we have four right triangles by drawing the two diagonals. If you see closer, we can use the Pythagorean Theorem, to find the side length, which is $$\sqrt{20^2+21^2}=\boxed{29}.$$

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Apr 21, 2019
#2
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To solve this problem, use the formula to find the side length of a rhombus. This is because we use the formula  $$a = \sqrt{{p}^{2}+(4*{a/p}^{2})}*1/2$$

in which a is the area and p is the diagonal. After the evaluation, we get a total of 29.

~~Hypotenuisance

Apr 21, 2019