Question

The surface area of a cuboidal box is y^2-2y-15.The box has a square base whose length is y+3. Find the height?

Answer 1

let  height be = h
Surface Area of cuboid= 2(y+3)² + 4(y+3)h
From Question we have  2(y+3)²+ 4(y+3) h=y²-2y-15
                                   ⇒    (y+3)( 2y+6+4h) = y²+3y -5y -15= y(y+3) -5(y+3)
                                   ⇒    (y+3)(2y+6+4h)=(y-5)(y+3)
                                   ⇒     2y+6+4h=y-5
                                   ⇒     4h= -y-11
                                   ⇒      h= - (y+11)/4