Question

A wallpaper of 312cm long and 25cm wide is used to cover the walls of a room of length 7m. If the breadth is twice it's height, then find it's height.

Answer 1

A wallpaper of 312cm long and 25cm wide is used to cover the walls of a room of length 7m. If the breadth is twice it's height, then find it's height.

**Solution:**

Let the height of the room be h, then its breadth is 2h.

**Area of the walls of the room is**

$$A = 2lh + 2bh$$ $$l = 7m, b = 2h$$ $$A_1 = (14h + 4h^2) m^2$$

**Area of the wallpaper is**

$$A_2 = 3.12 * 0.25 = 0.78 m^2$$ $$A_1 = A_2$$ $$14h + 4h^2 = 0.78$$ $$2h^2 + 7h - 0.39 = 0$$ $$h = 0.055m$$

It is not possible, so input data were not correct.

If we will take wallpaper being 3120 inch long and 25 inch wide, then

$$A_2 = 3120 * 25 = 78000 \text{ inch}^2 = 50.32 m^2$$ $$4h^2 + 14h - 50.32 = 0$$ $$h = 2.2m$$

**Answer:** The height of a room is 2.2 m.