The right angles triangle has three sides including the hypotenuse which is opposite to the right angle. If the hypotenuse - H Then one side is - H - 2 Third side is 7 cm shorter then H-2 Therefore it’s H -2-7 = H -9 According to Pythagoras theorem Square of hypotenuse = sum of the squares of the other 2 sides H² = (H-9)² + (H-2)² H² = H² -18H + 81 + H² -4H + 4 0 =H² -22H +85 This is a quadratic equation 0 = H² - 17H -5H +85 0 = H (H - 17) -5(H-17) (H-17) (H-5) =0 H -17=0 or H-5=0 H could be 17 cm or 5 cm If H =5 cm then Side 1 -H-2 = 3 cm And side 2 - H-9 = -4 cm Since lengths cannot be negative values H isn’t 5 cm Therefore H =17 cm 1 side is H-2 = 15 cm 2nd side H -9 = 8 cm Three sides are 17 cm, 15 cm and 8 cm
