Question

The length and breadth of a cuboid are in the ratio 4:5. The height and total
surface area of the cuboid are 18 cm and 3384 cm” respectively. Find its length and breadth.

with explaination​

Answer 1

Answer:

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Step-by-step explanation:

so here length and breadth of cuboid are in the ratio 4:5

so let common multiple be k

thus length(l)=4k

breadth(b)=5k

height(h)=18.cm

so we know that

total surface area of cuboid=2(lb+bh+lh)

so here

total surface area of cuboid=3384 cm.square

thus then accordingly

3384=2[(4k×5k+)+(5k×18)+(4k×18)]

ie 1692=20k.square+90k+72k

ie 20k.square+162k-1692=0

so dividing by 2 on both sides

we get

10k.square+81k-846=0

so then

by using discriminant formula and solving this quadratic equation by formula method

we get

k=6 or k=-14.1

but as dimensions,length of any geometric figure are never negative

k=-14.1 is absurd

thus k=6

substitute value of k in missing terms

we get

length(l)=4k

=4×6

length(l)=24.cm

similarly breadth(b)=5k=5×6

breadth(b)=30.cm