Question 57

The surface area of a cuboidal box is 240 $$cm^2$$ and the length of its diagonal is 11 cm. What is the sum (in cm)of its length, breadth and depth?

Solution

The diagonal, $$d$$ of cuboid = $$\sqrt{l^2+b^2+h^2}$$

=> $$l^2+b^2+h^2=121$$ -------------(i)

Also, Surface area = $$2(lb+bh+hl)=240$$ -------------(ii)

Now, sum of length, breadth and height = $$(l+b+h)^2=(l^2+b^2+h^2)+2(lb+bh+hl)$$

Substituting values from equation (i) and (ii), we get :

=> $$(l+b+h)^2=121+240=361$$

=> $$(l+b+h)=\sqrt{361}=19$$ cm

=> Ans - (B)

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