Question

The hypotenuse of a right triangle measures 20cm. The sum of the lengths of the other two sides is 28cm. Find the lengths of those two sides.

Answer 1

Step-by-step explanation:

Here,

h = 20cm

By question,

p + b = 28cm

or, p = 28 - b

Using pythagoras theorem,

h^2 =p^2 + b^2

20^2 = (28-b) ^2 + b^2

400 = 28^2 -2x28xb + b^2 + b^2

56b = 784 - 400 + 2 b^2

0 = 2b^2 - 56b + 384

0 = 2 ( b^2 - 28b + 192)

0 = b^2 - (16 + 12) b + 192

0 = b^2 - 16b - 12b + 192

0 = b (b - 16) - 12 (b - 16)

0 = (b - 16) (b - 12)

Either,

b= 16

Or,

b = 12

When b = 16,

p = 28 - 16

= 12

When b = 12,

p = 28 - 12

= 16