the perimeters of 2 squares are in a ratio of 4 to 9. what is the ratio between the areas of the 2 squares?
a. 2 to 3
b. 4 to 9
c. 16 to 27
d. 16 to 81
I dont understand how to work out this problem >.< so please explain to me how you got the answer...? I dont quite get it..
2007-04-12 12:28:59 · 5 answers · asked by magik ;) 5 in Education & Reference ➔ Homework Help
The area of any rectangle is calculated by multiplying the length by the width. In a square, length and width are the same, so the area is the square (multiplied by itself) of a side. Perimeter is just the sum of the sides. So if the perimeters are in the ratio of 4 to 9, the areas will be in the ratio of (4 X 4) (that's 4 squared) to (9 X 9) (9 squared), or 16 to 81.
2007-04-12 12:36:09 · answer #1 · answered by thesbrian 2 · 1⤊ 0⤋
I am not sure this is the right way to do it, but this is what I did. Since squares have equal sized sides, I started that the sides were 4 and 9. That gave a perimeter of 16 (4+4+4+4) and 36 (9+9+9+9). I then divided 16 and 36 by 4, getting 4 and 9, proving that ratio. I then calculated the area of each square by mutliplying the value of 2 sides, so the square with sides = 4 had an area of 16 (4X4), while the square with 9 had an area of 81 (9x9). Based on this, the ratio of the areas is 16 to 81.
Hope this helps
2007-04-12 12:38:10 · answer #2 · answered by Mike J 4 · 0⤊ 0⤋
the answer is D because if two squares' perimeter are in a ration of 4 to 9, you can have 2 squares with perimeters of 8 and 18. 8/18 equals 4/9. if that were true then the each side of the smaller square is 2 (8 divide by the 4 sides of square), each side fo the larger square is 4.5. (18 divide by 4 sides). If you square 2 and 4.5 to get the area, you end up with 4 and 20.25. and if you multiple the two by 4, it will give a ratio of 16 to 81.
2007-04-12 12:37:01 · answer #3 · answered by tmacfan1121 2 · 0⤊ 0⤋
Because area comes in square units, you must square (multiply by itself) the ratio of the perimeters or sides, which are not in square units.
So 4^2 to 9^2 = 16 to 81
2007-04-12 12:36:53 · answer #4 · answered by hayharbr 7 · 0⤊ 0⤋
A slightly different approach:
For a square P = 4s.
so s = P/4
A = s^2 = P^2/16
A1/A2 = (P1^2/16)(P2^2/16) =
A1/A2 = (P1^2)/(P2)^2
A1/A2 = (P1/P2)^2
A1/A2 = (4/9)^2
A1/A2 = 16/81
2007-04-12 12:47:59 · answer #5 · answered by Helmut 7 · 0⤊ 0⤋