• # question_answer If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is A)  $351\,\,c{{m}^{2}}$ B)  $256\,\,c{{m}^{2}}$ C)  $265\,\,c{{m}^{2}}$  D)  $315\,\,c{{m}^{2}}$

[a] Let length=l, breadth=b, height=h. L+b+h=24 (given)         ... (i) Diagonal of parallellopiped=15 cm $\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}=15\,\,or\,\,{{l}^{2}}+{{b}^{2}}+{{h}^{2}}=225$ Squaring eqn. (i) on both sides ${{l}^{2}}+{{b}^{2}}+{{h}^{2}}+2lb+2bh+2hl=576$ $2\,\,(lb+bh+hl)=576-\,225=351$ $[\therefore$Surface area of parallellopiped $=2\,\,(lb+bh+hl)]$