If the length, breadth and total surface area of a cuboid are 15 cm, 10 cm and 1300$c{m}^2$ , then its height is

Given:

• Length of the cuboid: 15 cm
• Breadth of the cuboid: 10 cm
• Total Surface Area (T.S.A.): 1300 cm²

Formula for Total Surface Area of a Cuboid:

The total surface area of a cuboid is given by the formula

 T.S.A. = 2(lb + bh + hl)

where l is the length, b is the breadth, and h is the height of the cuboid.

Substitute the Given Values:

Substituting the length and breadth into the formula along with the T.S.A., we have

2(15 × 10 + 10 × h + 15 × h) = 1300

Step-by-step calculation:

First, calculate the product of length and breadth:

15 × 10 = 150

Now substitute this value into the equation:

2(150 + 10h + 15h) = 1300

Simplify the terms inside the parentheses:

150 + 10h + 15h = 150 + 25h

The equation becomes:

2(150 + 25h) = 1300

Expand and simplify:

300 + 50h = 1300

Isolate the term with h:

50h = 1300 - 300

50h = 1000

Divide by 50 to find h:

h = 1000 ÷ 50 = 20

Conclusion:

Using the provided length and breadth values, along with the total surface area, we calculate that the height of the cuboid is 20 cm.