Question

a rectangle has a diagonal 20 inches long that forms angles of 60 and 30 with the sides. find the perimeter of the rectangle.

Answer 1

Answer:

P = 47.32

Step-by-step explanation:

This triangle is a special triangle. Because it is 30-60-90 it will have measurements similar to $1 - \sqrt{3} - 2$. If the longest side is 20 then it corresponds to 2. This means the shortest side of 1 corresponds to half this or 10.

So the triangle will have sides $10 - 10\sqrt{3}  - 20$.

To find the perimeter add all these lengths.

$P = 10 + 10\sqrt{3} +20\\P = 30+10\sqrt{3} \\ P = 47.32$