d) 12
Step-by-step explanation:
Given:
Right triangle with side 9+7=16
let the third side of bigger triangle be y
and perpendicular line between 9 and 7 be z
Now:
By Pythagoras theorem:
(16)^2=x^2+y^2
x^2=256-y^2
Also
y^2=z^2 +7^2
z^2=y^2-49
and
x^2=9^2 + z^2
Now substituting z^2=y^2-49 in above we get:
x^2=81 + y^2-49
x^2=32+y^2
Adding x^2=256-y^2 and x^2=32+y^2 we get:
2x^2= 288
x^2=144
x=12 !