Problem:

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

Guest Apr 21, 2019

#1**+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 \(\sqrt{20^2+21^2}=\boxed{29}.\)

.tertre Apr 21, 2019

#2**-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

Hypotenuisance Apr 21, 2019