Please answer 9 with explanation Share with your friends Share 2 Neha Sethi answered this Let the length ,width and height of cuboid be x,y and zIt has 3 different areas and perimetersTop and bottom has same area and perimeter, front and back has the same area and perimeter and right and left has same area and perimeterA.T.Q2x+y+xy=16 ...iand 2y+z+yz=24 ⇒2y+2z+yz=24⇒z=24-2y2+y ...iiand 2z+x+zx=31⇒2z+2x+zx=31⇒z=31-2x2+x ...iiiFrom 2 and 3, we get24-2y2+y=31-2x2+x⇒24-2y2+x=31-2x2+ySolving this we get⇒48+24x-4y-2xy=62+31y-4x-2xy⇒48+24x-4y=62+31y-4x⇒28x=35y+14⇒4x=5y+2x=5y+24 ....ivFrom 1 and 4, we get25y+24+y+5y+24×y=16⇒25y+2+4y4+5y2+2y4=16⇒29y+24+5y2+2y4=16⇒18y+4+5y2+2y=64⇒5y2+20y-60=0⇒y2+4y-12=0⇒y2-2y+6y-12=0⇒yy-2+6y-2=0⇒y+6y-2=0⇒y+6=0 or y-2=0⇒y=-6 ignored as width cannot be negative,2So, y=2If y=2 then x=52+24 =3 from ivFrom 2, z=24-222+2=5So, x=3,y=2 and z=5Volume =xyz=30 which lies between 28 aand 35Hence correct option is D 1 View Full Answer
