Question

In a right angled triangle with legs of lengths `a, b` and hypotenuse of length `c`, we are told that `b = 16"cm"` and `a+c = 32"cm"`. What are the values of `a` and `c` ?

Answer 1

`a=12`cm and `c=20`cm

Explanation:

We are given:

`b=16`

`a+c=32" "` and hence `" "c = 32-a`

From Pythagoras, we know that:

`c^2 = a^2+b^2`

So putting `c=32-a` and `b=16`, we have:

`(32-a)^2 = a^2+16^2`

That is:

`1024-64a+a^2 = a^2+256`

Subtract `a^2` from both sides to get:

`1024-64a = 256`

Add `64a-256` to both sides to get:

`768 = 64a`

Transpose and divide both sides by `64` to get:

`a = 12`

Then:

`c = 32-a = 32-12 = 20`

So:

`a=12`cm and `c=20`cm