Question

The hypotenuse of a right triangle is $10$ inches and the radius of the inscribed circle is $1$ inch. The perimeter of the triangle in inches is:

$15$

$22$

$24$

$26$

$30$

For a right triangle with legs $a,b$ and hypotenuse $c,$ the inradius is $\frac{a+b-c}{2}$

Substitute $r=1$ and $c=10$ to find $a+b$

For a right triangle, $r=\frac{a+b-c}{2}.$ With $r=1$ and $c=10,$ this gives $a+b=12.$ Hence the perimeter is $a+b+c=12+10=22.$

Thus, the correct answer is B.