find the area of the largest rectangle that can be inscribed in an isosceles triangle of base10ft. and area 30 square ft

Thats 15 sq. feet (according to me)

let the length of the part of base, not included in side of Rectangle be X both side and the vertical side length be Y......

Now the rectangle has side lengths, Y and 10-2X.......

now use similar triangle property to find relation b/w Y and X

i.e. Y=6X/5

Hence area = XxY = 6X/5x(10-2X)

Use dA/dX=0 to get X=5/2

Therefore, A=15................