Need Answer Quick ,please!?
Can the floor of a 15-foot by 20-foot rectangular den be completely covered with whole tiles which are 8-inch squares?
If so, how many of these will be needed? Draw a picture to show how they would be arranged.
If the floor cannot be completely covered with whole tiles, what is the maximum number of whole tiles that can be laid on the floor? Draw a picture to show how this maximum number could be arranged?
***Please show me how you got your answer 10 POINTS!
20′ = 240″ = 30 – 8″ squares
15′ = 180″ 22.5 – 8″ squares
So 30 columns with 22 rows
The last row of 30 is 1/2 squares
You would need 660 whole tiles and 30 1/2 tiles for the last row
Draw your picture like this
30 columns across of boxes
with 22 rows down.
The last row should be a 1/2 size box.
Well first, make everything the same units, so convert ft into inches.
(1 ft = 12 inches)
so now you have a 180″ x 240″ rectangle
divide both sides by 8 and see if they’re whole numbers
180/8 = 22.5 and 240/8 = 30
in this case 180 does not dived by 8 evenly so you take the closest whole number lower than the fraction.
so 22×30 tiles with a 4 inch gap on one side of the rectangle.
change feet to inches
for 15 feet across: you get 15 *12=180 inches across the room
you have 8 inch tiles. So 180/8=22.5. Therefore you can only put 22 tiles across.
the vertical part of the room is 20 feet.
change to inches.
20 feet is 240 inches. Divide by 8 is 30 square down.
so draw 22 squares across and 30 squares down.
22 x 30 = 660 maximum 8 inch squares
First, find the area of the garden. Remember to convert feet to inches (or vice versa) so that the units are all the same, or else your answer will be wrong. I prefer to go with feet to inches, though.
15 ft = 180 in
20 ft = 240 in
180 x 240 = 43200 inches squared is your area
Now, to check if the 8 inch squares can fit, divide them. If it’s a whole number, that means it’s a perfect fit.
43200/8 = 5400 (perfect fit)
So 5400 tiles can fit in your garden. Now to find out which tiles go in which side…
We need to know the length of each side of the 8 inch-squared tiles, so find the squared root of that, and that’s just about 2.83. If you don’t believe me, try 2.83 x 2.83 and you get 8.
Now, let’s see how many tiles can fit along the side that’s 180 inches long.
180/2.83 = 63.6 tiles
Now for the other side
240/2.83 = 84.8 tiles
These numbers might be a bit weird because I rounded, but that’s just the basis of it. Try rounding the 2.8284271247461900976… better and you should get whole numbers for answers (that’s what you should get, since exactly 5400 tiles should fit). I’m pretty sure I’m right, so remember to check my math and my logic.
Good Luck!
Answer of the first part is : no
In the length direction you can lay:
(20 feet x 12 inches) = 240 inches / 8 = 30 tiles
In the width direction you can lay:
15 x 12 = 180/8 = 22.5 tiles
Thus the answer is no
The maximum whole tiles will be:
30 x 22 = 660 tiles