Question

Length and breadth of a cuboid is in the ratio of 4:5 and its height is 18 cm. Its Total surface area is 3384 cm2. Find itsLength and breadth.

Answer 1

Answer:

Step-by-step explanation:We have the ratio of length to that of the breadth of the cuboid as 4:5. Since length is greater than breadth so let the length of the cuboid be 5x and the breadth be 4x.

We have, l=5x, b=4x and h= 18 cm

Now, total surface area of the cuboid=3384 cm sq.

So, 2(lb+bh+hl)=3384

2{(5x)(4x)+(4x)(18)+(18)(5x)}=3384

2(20x sq + 72x + 90x)=3384

20x sq+162x=1692

20x sq + 162x - 1692=0

Dividing b/s by 2, we get

10x sq+ 81x - 846=0

Splitting the middle term, we get

10x sq-60x+141x-846=0

10x(x-6)+141(x-6)=0

(10x+141)(x-6)=0

So, 10x+141=0 or x-6=0

x=-141/10 or x=6

Since x is a measure for the length, it cannot be negative.

So, x=6

Therefore, length= 5x=5(6)=30 cm

and, breadth=4x=4(6)=24 cm