If the sides of an equilateral triangle are increased by 7 inches, 4 inches and 1 inch respectively, a right triangle is formed. Find the length of a side of the equilateral triangle.

Answer 1

x = length of sides of equilateral triangle.

x+1, x+4, x+7 = lengths of sides of expanded triangle

if right triangle x+7 (longest side) will be hypotenuse and x+1 and x+4 will be legs

Per Pythagorean Theorem (x+1)^2 + (x+4)^2 = (x+7)^2

x^2 + 2x + 1 + x^2 + 8x + 16 = x^2 + 14x + 49

2x^2 + 10x + 17 = x^2 + 14x + 49

x^2 -4x -32 = 0

(x-8)(x+4) = 0

x = 8 length of side of equilateral triangle