Answer:
8, 15 and 17 feet respectively
Step-by-step explanation:
Let the shorter leg=l feet
The longer leg of a right triangle is 7 ft longer than the shorter leg, therefore Length of the longer leg=(l+7) feet
The hypotenuse is 9ft longer than the shorter leg. Therefore Length of the hypotenuse=(l+9) feet
Using Pythagoras Theorem
[tex]Hyp^2=Opp^2+Adj^2\\(l+9)^2=l^2+(l+7)^2\\(l+9)(l+9)=l^2+(l+7)(l+7)\\l^2+9l+9l+81=l^2+l^2+7l+7l+49\\l^2+18l+81=2l^2+14l+49[/tex]
This results into:
[tex]2l^2-l^2+14l-18l-81+49=0[/tex]
[tex]l^2-4l-32=0\\l^2-8l+4l-32=0\\l(l-8)+4(l-8)=0\\(l-8)(l+4)=0[/tex]
l-8=0 or l+4=0
l=8 or -4
Since length cannot be negative, The length l=8 feet
The sides of the rectangle are therefore: 8, 15 and 17 feet respectively
