The length of cuboid is 16 cm and breadth of cuboid is 4 cm.
A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (L), Breadth (B), and Height (H) of the cuboid and use the formula, SA=2 x ( LB + BH + HL ) , to find the surface area.
Here, We have given that height of the cuboid is 5cm.
Let length of the cuboid = X cm
so, the breadth of the cuboid = [tex]\frac{X}{4}[/tex] cm
also, we have given that total surface area is 328 cm²
Now, put all the values in the formula of Surface Area (SA):
SA = 2 x ( LB + BH + HL )
SA = 2 x ( X²/4 + 5X/4 + 5X )
SA = 2 x ( ( X² + 5X + 20X) / 4 )
SA = ( X² + 5X + 20X ) / 2
X² + 5X + 20X = 328 x 2
X² + 25X = 656
X² + 25X - 656 = 0
using Quadratic Formula: see the attached figure for the formula.
here Discriminant D = b² - 4ac
D = 625 - 4(-656)
D = 3249
on putting value of D or b² - 4ac in the formula we get
X = ( -25 + 57 ) / 2 and ( -25 - 57 ) /2
length can not be negative so we eliminate the second answer.
now, X = 16 cm
breadth = X /4 = 4 cm
Hence, The length of cuboid is 16 cm and breadth of cuboid is 4 cm.
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