Question

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m^2. Find the dimensions of cuboid​

Answer 1

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Ratio of the dimensions of a cuboid = 1:2:3

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The dimensions of the cuboid i.e length, breadth and height

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Since, the dimensions of the cuboid are in the ratio 1:2:3. So, let the dimensions be x, 2x, 3x in metres.

Now,

Surface area of cuboid = 2(lb + bh + lh)

Given, surface area = 88${m}^{2}$

$\implies 2(x×2x + 2x×3x + 2x×x) = 88 \\ \\</p><p></p><p>\implies 2(2{x}^{2}+ 6{x}^{2} + 3{x}^{2}) = 88 \\ \\</p><p></p><p>\implies 2 × 11{x}^{2} = 88 \\ \\</p><p></p><p>\implies 22{x}^{2} = 88 \\ \\</p><p></p><p>\implies {x}^{2} = \frac {88}{22} \implies {x}^{2} = 4 \\ \\</p><p></p><p>\implies {x}^{2} = {2}^{2} \\ \\</p><p></p><p>\implies x = 2m$

2x = 2×2 = 4m, 3x = 3×2 = 6m

Hence, the dimensions are 2m, 4m and 6m

________________

Formula used:-

• Surface area of cuboid = 2(lb + bh + lh)

________________

${\pink{\underline{\underline{\bold{Additional\:Information:-}}}}}$

Let the dimensions of cuboid of length (l) , breadth (b) and height (h)

• Total surface area if cuboid = 2(lb + bh + lh)
• Lateral surface area of cuboid = 2(l + b) h
• Diagonal of cuboid = $\sqrt { {l}^{2}+{b}^{2}+{h}^{2}}$
• Length of all 12 edges of the cuboid = 4(l+b+h)

Answer 2

Step-by-step explanation:

YOUR ANSWER IS IN THE ATTACHMENT