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# Geometry

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137
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Two diagonals of a parallelogram have lengths 6 and $$10$$. What is the largest possible length of the shortest side of the parallelogram?

Jan 29, 2022

#1
+13887
+1

What is the largest possible length of the shortest side of the parallelogram?

Hello Guest!

The longest side of the parallelogram is when the diagonals are perpendicular to each other. It will be a four-sided rhombus. The length of the sides is

$$s=\sqrt{(\frac{10}{2})^2+(\frac{6}{2})^2}\\ \color{blue}s=5.831$$

!

Jan 29, 2022
#2
+361
+2

In radical form, it would be $$\frac{\sqrt{136}}{4}$$

or, $$\frac{2\sqrt{34}}{4}$$or $$\frac{\sqrt{34}}{2}$$

Jan 29, 2022