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# ?

1 Answer
Dec 13, 2017

#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