Question

The sides of an equilateral triangle are reduced by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed. Find the length of each side of the equilateral triangle?

Answer 1

the length of each side of the equilateral triangle = 17

Explanation:

suppose the side length of equilateral triangle = x

The 3 side of right triangle formed (by side length): x-12 , x-13, x-14

(x-13)² + (x-14)² = (x-12)² .... Pythagorean theorem

x² -26x + 169 + x² -28x + 196 = x² -24x + 144

x² - 30x +221 = 0

(x- 17) (x - 13) = 0

x = 17 or x = 13

if x = 13 the right triangle will have a side length of 13-13=0 ... not solution

x = 17

check: 17-12=5 17-13=4 17-14=3

3²+4² = 25 = 5²