The shorter leg of a right triangle is 7 nanometers shorter than its longer leg. Its hypotenuse is 1 nanometer longer than its longer leg. Give the length of the triangle's hypotenuse

Answer 1

b: length of the longer leg. a = (b-7) , c = (b+1)

(b-7)² + b² = (b+1)²

b² - 14b + 49 + b² = b² + 2b + 1

b² - 16b + 48 = 0

(b - 4)(b - 12) = 0

b = 4 or b = 12 but b ≠ 4 since that would make a < 0.

a = 5 , b = 12 , c = 13. The hypotenuse is 13 nanometers.