Question

If the sides of a right angles triangle are in A.P., then the sides are proportional to.

• A. $1:2:3$
• B. $2:3:4$
• C. $3:4:5$
• D. $4:5:6$

Answer 1

The correct option is C $3:4:5$

Let the sides of the triangle be $x,y,z$

with$z>x$ and $y$

since the sides are in AP

$z=x+2d$ where d is the common difference

By Pythagoras theorem

$z^2=x^2+y^2$

$(x+2d{)}^2=x^2+(x+d{)}^2$

simplifying we get

$x^2-2dx-3d^2=0$

after solving we get

$x=3d$ and $x=-d$

now $x=3d$ ,$y=4d$ and $z=5d$

so $x:y:z:=3:4:5$

so option C is correct.