If U is the a point in the interior of an equilateral triangle whose side is 20cm, then what is the sum of distances from U to each sides of AABC?

17.32 cm

Step-by-step explanation:

According to Viviani's theorem, the sum of the distances from an interior point to the sides of an equilateral triangle equals the height of the triangle.

In an equilateral triangle ΔABC, if U is an interior point, the sum of distances from  U to each sides of ΔABC = height of triangle. Since each side of the triangle is 20 cm, we can find the height of the triangle (h)

This can be represented by a triangle with hypotenuse 20 cm, a leg of 10 cm (20/2) and the other leg h cm. Using Pythagorean theorem:

h² + 10² = 20²

h² = 400 - 100 = 300

h = √300 = 17.32 cm

Therefore, the sum of distances from  U to each sides of ΔABC is 17.32 cm

answer: h

step-by-step explanation: