The problem describes a tile that is cut into four parts. We need to: (a) Form an expression for the area of the tile, L, in terms of y. (b) Given that the area of the tile is 6175 $cm^2$, find the value of y. (c) The smallest piece of the tile is used to decorate a school wall. Find the number of such pieces needed if the area of the wall to be decorated is 1.08 $m^2$.

1. Problem Description

The problem describes a tile that is cut into four parts. We need to:

(a) Form an expression for the area of the tile, L, in terms of y.

(b) Given that the area of the tile is 6175 $cm^2$, find the value of y.

(c) The smallest piece of the tile is used to decorate a school wall. Find the number of such pieces needed if the area of the wall to be decorated is 1.08 $m^2$.

2. Solution Steps

(a) The tile has dimensions (35 + y) cm and 65 cm.

Area of the tile, L = length * width.

$L = (35 + y) * 65$

$L = 2275 + 65y$

(b) We are given that the area of the tile is 6175 $cm^2$.

Therefore, $L = 6175$.

$6175 = 2275 + 65y$

$65y = 6175 - 2275$

$65y = 3900$

$y = \frac{3900}{65}$

$y = 60$

(c) The smallest piece of the tile has dimensions y cm by y cm. Since $y = 60$, the smallest piece is a square with sides 60 cm.

Area of the smallest piece $= y^2 = 60^2 = 3600 cm^2$.

The area of the wall to be decorated is 1.08 $m^2$. We need to convert this to $cm^2$.

1 $m = 100 cm$.

1 $m^2 = (100 cm)^2 = 10000 cm^2$.

Area of the wall $= 1.08 m^2 = 1.08 * 10000 cm^2 = 10800 cm^2$.

Number of pieces needed $= \frac{Area \ of \ the \ wall}{Area \ of \ the \ smallest \ piece} = \frac{10800}{3600} = 3$.

3. Final Answer

(a) $L = 2275 + 65y$

(b) $y = 60$

(c) 3