Determine the length and the lateral surface area of a cuboid whose lateral surface area is 880 sq. ft and whose breadth and height are 12 ft and 20 ft, respectively.

The given values are

Lateral surface area = 880 sq.ft, h = 20 ft and w = 12 ft

The lateral surface area of the cuboid is

\$"Lateral surface area" = 2"h" ("w" + "l")\$

So we can rearrange the formula to solve for l

\$"l" = (("lateral surface area")/(2"h")) - "w"\$

Now plug the values in the formula

\$"l" = ((880)/2 times 20) - 12\$

After simplification

⇒ l = 22 - 12
⇒ l = 10 ft

The total surface area of a cuboid is

\$"Total surface area" = 2"lw" + 2"lh" + 2"wh"\$

Now plug the values in the formula

\$"Total surface area" = 2 times 10 times 12 + 2 times 10 times 20 + 2 times 12 times 20\$

Make it simpler

\$"Total surfcae area" = 240 + 400 + 480\$

After simplification

Total surfcae area = 1120 sq.ft

So, the length of the cuboid is 1010 ft and the total surface area is 1120 sq. ft

Can you summarize what you’ve understood in the above steps?

This is incorrect because it does not satisfies the conditions given in the problem

10 ft and 1210 sq.ft

This is incorrect because it does not satisfies the conditions given in the problem

10 ft and 1102 sq.ft

This is correct because it satisfies the conditions given in the problem

10 ft and 1120 sq.ft

This is incorrect because it does not satisfies the conditions given in the problem

10 ft and 1201 sq.ft

Option

C

Can you summarize what you’ve understood in the above steps?