Question 1076331

a right triangle, => so, use Pythagorean theorem

{{{c^2=a^2+b^2}}} where {{{a}}} and {{{b}}} are legs and {{{c}}} hypotenuse


the lengths of the legs are represented by {{{a=7}}} and {{{b=r}}}, and the hypotenuse is represented by {{{c=r + 1}}}:

{{{c^2=a^2+b^2}}}

{{{(r + 1)^2=7^2+r^2}}}

{{{r^2 +2r+ 1=49+r^2}}}

{{{cross(r^2) +2r+ 1=49+cross(r^2)}}}

{{{2r=49-1}}}

{{{2r=48}}}

{{{r=48/2}}}

{{{r=24}}}

now find hypotenuse:

 {{{c=r + 1}}}=> {{{c=24 + 1}}}=> {{{highlight(c=25)}}}