Problem:
A rhombus with area 840 has a diagonal of length 40 . What is its side length?
+4609 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 \(\sqrt{20^2+21^2}=\boxed{29}.\)
+220 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
