Question

A room is 12 m long and the width is 1.5 m more than the height. If the area of the four walls is 105 m², find the height of the room giving your answer correct to 2 decimal places.​

Answer 1

Explanation:

Let's start by finding the width of the room in terms of its height.

Let the height of the room be h meters. Then the width of the room is (h + 1.5) meters.

The area of the four walls is equal to the perimeter of the room multiplied by the height of the room. The perimeter of the room is:

2(length + width) = 2(12 + h + 1.5) = 2(h + 13.5)

So, the area of the four walls is:

2(h + 13.5)h + 2(h + 13.5)(h + 1.5) = 105

Simplifying and solving for h, we get:

2h^2 + 27h - 60 = 0

Using the quadratic formula, we get:

h = (-b ± sqrt(b^2 - 4ac))/(2a)

where a = 2, b = 27, and c = -60.

Plugging in the values, we get:

h = (-27 ± sqrt(27^2 - 4(2)(-60)))/(2(2))

h = (-27 ± sqrt(1101))/4

h ≈ 2.34 or h ≈ -12.84

We can ignore the negative solution since the height of the room must be positive. Therefore, the height of the room is approximately 2.34 meters, rounded to two decimal places.