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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
avatar+4325 
+3

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
avatar+128 
-2

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

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