Question

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse. Find the length of the hypotenuse

Answer 1

25cm

Explanation:

the relationship between the sides of a right angle triangle was defined by Pythagoras in this theorem which states that where a, b, and c are the lengths of the sides of a right angled triangle,

a² + b² = c²

Where c is the length of the hypotenuse side and a and b are the lengths of the other 2 sides. As such,

let the hypotenuse side in length be c,

(c - 5)² + (c - 10)² = c²

c² - 10c + 25 + c² - 20c +100 = c²

c² - 30c + 125 = 0

c² - 25c - 5c + 125 = 0

factorizing

(c - 25)(c -5) = 0

c = 25cm or 5cm

However, the length of the hypotenuse cannot be 5cm otherwise other sides would be negative.

Answer 2

Answer: hypotenuse = 25 cm

Explanation:

Let h represent the length of the hypotenuse.

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse. It means that the length of the leg is

(h - 5) cm

The other leg is 10 cm smaller than the hypotenuse. It means that the length of the other leg is

(h - 10) cm

We would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

h² = (h - 10)² + (h - 5)²

h² = (h - 10)(h - 10) + (h - 5)(h - 5)

h² = h² - 10h - 10h + 100 + h² - 5h - 5h + 25

h² = h² + h² - 20h - 10h + 100 + 25

h² = 2h² - 30h + 125

2h² - h² - 30h + 125 = 0

h² - 30h + 125 = 0

h² - 25h - 5h + 125 = 0

h(h - 25) - 5(h - 25) = 0

h - 25 = 0 or h - 5 = 0

h = 25 or h = 5

The hypotenuse is 25 cm since it is longer