×24 = 8 cm Hypotenuse = √82+62 = √64+36 = 10 cm
Let altitude to hypotenuse = h h = √36−x2 ... (1) and h = √64−(10−x)2 ... (2) Equating (1) and (2) we get: √36−x2 = √64−(10−x)2 36−x2 = 64 - 100 - x2 + 20x 36−x2 = −36−x2+20x 72 = 20x ⇒ x = 3.6 b = √36−(3.6)2 = √36−12.96 = √23.04 = 4.8 cm