Question

the length breath and hight of a cuboid are in the 5:4:2 if the total surface area is 1216 cm² find the dimension of the solid

Answer 1

given that
length : breath : height = 5:4:2
let constant be x
so
length=5x
breadth=4x
height=2x

total surface area = 2(lb+bh+hl)
$2(20 {x}^{2} + 8 {x}^{2} + 10 {x}^{2} ) \\ 2(38 {x}^{2} ) \\ 76 {x}^{2}$
given TSA =1216 cm2
i.e. 76 x^2=1216
$i.e. {x}^{2} = 16 \\ x = 4$
So
length=5x=5×4=20cm
breadth=4x=4×4=16cm
height=2x=2×4=8cm