One of the students wants to make a tabletop shaped like a right triangle the tabletop will have the same area as the tabletop shown what are the set of possible lengths for the sides of the tabletop that meet in a right angle answer today

The area of the given figure is equal to the area of a rectangle with sides 5 feets by 6 feets less the area of four square cut-outs of side 1 feet.
Area of the rectangle = 5 x 6 = 30 square feets.
Area of the four square cut-outs = 4(1 x 1) = 4 x 1 = 4 square feet
Area of the given figure = 30 - 4 = 26 square feet.

Area of a triangle = 1/2 x base x height
i.e. 1/2 bh = 26
bh = 26 x 2 = 52
possible values of base and height = (1 and 52), (2 and 26), (4 and 13)