Question

In a rectangular solid l : b : h = 4 : 3 : 2. If the total surface area is 1300 cm², find its dimensions.

Answer 1

We have,

In a rectangular solid l : b : h = 4 : 3 : 2. If the total surface area is 1300 cm²,

Let the length of the rectangular solid be 4x cm

The breadth of the rectangular solid be 3x cm

And the height of the rectangular solid be 2x cm

Now, the total surface area of the rectangular solid is 2(lb + bh + hl), where l is the length, b is the breadth and h is the height.

Then,

1300 = 2[(4x)(3x) + (3x)(2x) + (2x)(4x)]

1300 = 2(12x² + 6x² + 8x²)

1300 = 2(26x²)

x² = `1300/52` = 25

x = 5

Therefore, the dimensions of the rectangular solid are,

Length = 4 × 5 = 20 cm

Breadth = 3 × 5 = 15 cm

Height = 2 × 5 = 10 cm