A 15 foot by 18 foot porch floor is to be completely coverede with 1-foot square tiles. White tiles are to cover the center of the floor and green tiles are to form a 2-foot wide border around the white tiles. How many green tiles and how many white tiles will be needed?/. help plz. can you show work thanks very much.
First find the area of the porch floor A = 15 * 18 = 270 ft? The green tiles form a 2-ft wide border on all four sides of the floor. This means that the length will be 2-ft shorter at each end, and the width will be 2-ft narrower at each side, of the white portion. The length and width will be L = 18 - 2(2) = 18 - 4 = 14 feet long W = 15 - 2(2) = 15 - 4 = 11 feet wide and its area will be Aw = 11 * 14 = 154 ft? [Where Aw = area of white tiles] The area of the green portion, Ag, will be the total area, A, less the area of the white tiles, Aw Ag = A - Aw = 270 - 154 = 116 ft? [Where Ag = area of green tiles] Since the area of each tile is 1 ft?, this means that there will be 116 green tiles and 154 white ones.
Draw a picture and use practical thinking plus arithmetic. Then just add up the area of the sections of tile.
this is really just an area question. If it helps you to see it, grab a piece of graph paper. Each sqare represents one till. Mark of 18 tiles in one direction and 15 in the other. Complete the rectangle. Then, shade in the other 2 food wide border. That two tiles in each direction around the outside. Shade the other border. Those are your green tiles. What's the length and width of the inner (white tiles)? Find the area of the whole floor: 18 ft x 15 ft. = 270 tiles Find the area of the white part (unshaded center tiles). (18-2(2))(15-2(2)) = 116 tiles The area of the green part is the area of whole floor - area of white part o= area green part. Since the tiles are 1ft^2 the number of tiles is the same as the area in feet.
The total number of square foot tiles you will need is 15 * 18, or 270 tiles. That is also the area within the rectangle of the room. Now the green tiles denote the perimeter of the square with certain allowances for corners and the fact that the perimeter you are talking about is 2 tiles wide. The outermost perimeter (green tiles) is 18 by 15 feet and is calculated by (2 * L) + (2 * W) -4. or (2 * 18) + (2 * 15) -4. Simplifying it brings it to (36) + (30) -4, or 62. You are probably wondering about the -4. That is because each corner is counted twice (once for length and again for width) and you need to compensate for the duplication. Now for the inner perimeter. The size of the inner perimeter is reduced by 2 feet or 2 tiles since the rectangle is smaller, so the dimensions are now 16 by 13 feet. The formula is the same, (2 * L) + (2 * W) -4 but with the new numbers. (2 * 16) + (2 * 13) -4 Simplifying (32) + (26) -4 = 54 Adding the two perimeters together, 62 + 54 = 116 Green tiles. Subtract that from the total tiles used, 270 - 160 = 154 White tiles. Now try that with 9 inch tiles. z
