Question

the dimensions of a cuboid are in the ratio of 1 ratio 2 ratio 3 and its total surface area is 88 CM square then its lateral surface area

Answer 1

Let the dimensions be x, 2x and 3x. 

Total surface area of a cuboid = 2 (lb + bh + hl) = 2 (x*2x + 2x*3x + 3x*x) = 2 (2x2 +6x2 + 3x2) = 22x2

Given, TSA of the cuboid is 88cm2

22x2 = 88cm2

x2 = 88cm2/22 = 4cm2

x = 2cm

Therefore, the dimensions of the cuboid will be :-

x = 2cm

2x = 2*2cm = 4cm

3x = 3*2cm = 6cm

Thus, lateral surface area the cuboid = 2h(l+b) = 2×3(2+2)cm2 =6(4)=24cm2