A right angled triangle has 2 cm and 7 cm respectively less than its hypotenuse. Find the length of each side of the triangle to the nearest millimitre.

Answer 1

Hi, Alex. Here's how to do it.

Let the hypotenuse's length be h.

Then, the other 2 legs are h - 2 and h - 7, respectively.

By Pythagoras, (h - 2)² + (h - 7)² = h²

(h² - 4h + 4) + (h² -14h + 49) = h²

2h² - 18h + 53 = h²

h² - 18h + 53 = 0 This is a quadratic which we must solve by the quadratic formula

h = (18 ± √(18² - 4(1)(53))) / 2

= (18 ± √(224 - 212)) / 2

= (18 ± √12) / 2

= 9 + √3 or 9 -√3

= 10.73 cm or 7.27 cm

If the hypotenuse is 10.73 cm, the other 2 sides are 8.73 and 3.73 cm, respectively.

If the hypotenuse is 7.27 cm, the other 2 sides are 5.27 and 0.27 cm, respectively.