A rectangle with sides 8 cm and 6 cm and one with sides 10 cm and 9 cm. Find the ratio of the perimeter and the areas of each pair of figures.
Perimeter ratio = (2*8+2*6)/(2*10+2*9) = ?
Area ratio = (8*6)/(10*9) = ?
Why did the rectangle go on a diet? Because it wanted to reduce its "perimeter" inches! As for the area, well, that remains to be squared.
Now, let's calculating these ratios:
For the first pair, we have a rectangle with sides 8 cm and 6 cm. The perimeter is given by P = 2(length + width), so P = 2(8 + 6) = 2(14) = 28 cm. The area is A = length × width, so A = 8 × 6 = 48 cm².
For the second pair, we have a rectangle with sides 10 cm and 9 cm. The perimeter is given by P = 2(length + width), so P = 2(10 + 9) = 2(19) = 38 cm. The area is A = length × width, so A = 10 × 9 = 90 cm².
Comparing the perimeters, the ratio is 28/38, which simplifies to 14/19 (kind of like my sense of humor to some people). And for the areas, the ratio is 48/90, which can be simplified to 8/15 (just like trying to make a reasonable joke out of a bot).
I hope those ratios give you a proportionate amount of mathematical laughter!
To find the ratio of perimeter and area for each pair of figures, we need to calculate their perimeters and areas first.
For the rectangle with sides 8 cm and 6 cm:
Perimeter = 2(Length + Width) = 2(8 cm + 6 cm) = 2(14 cm) = 28 cm
Area = Length × Width = 8 cm × 6 cm = 48 cm²
For the rectangle with sides 10 cm and 9 cm:
Perimeter = 2(Length + Width) = 2(10 cm + 9 cm) = 2(19 cm) = 38 cm
Area = Length × Width = 10 cm × 9 cm = 90 cm²
Now, let's calculate the ratio of perimeter and area for each pair of rectangles:
For the first pair of rectangles:
Ratio of Perimeter = Perimeter of 8 cm × 6 cm rectangle / Perimeter of 10 cm × 9 cm rectangle
= 28 cm / 38 cm
= 14/19
Ratio of Area = Area of 8 cm × 6 cm rectangle / Area of 10 cm × 9 cm rectangle
= 48 cm² / 90 cm²
= 8/15
Therefore, the ratio of the perimeter of the first pair of rectangles is 14/19 and the ratio of the areas is 8/15.
To find the ratio of the perimeters, you need to calculate the perimeter of each rectangle. The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
For the first rectangle with sides 8 cm and 6 cm:
Perimeter = 2(8 cm + 6 cm)
Perimeter = 2(14 cm)
Perimeter = 28 cm
For the second rectangle with sides 10 cm and 9 cm:
Perimeter = 2(10 cm + 9 cm)
Perimeter = 2(19 cm)
Perimeter = 38 cm
Now, to find the ratio of the perimeters, divide the perimeter of the second rectangle by the perimeter of the first rectangle:
Ratio of perimeters = (38 cm) / (28 cm)
To find the ratio of the areas, you need to calculate the area of each rectangle. The area of a rectangle is given by the formula:
Area = length * width
For the first rectangle with sides 8 cm and 6 cm:
Area = 8 cm * 6 cm
Area = 48 cm^2
For the second rectangle with sides 10 cm and 9 cm:
Area = 10 cm * 9 cm
Area = 90 cm^2
Now, to find the ratio of the areas, divide the area of the second rectangle by the area of the first rectangle:
Ratio of areas = (90 cm^2) / (48 cm^2)
So the ratios are as follows:
Ratio of perimeters = 38 cm / 28 cm
Ratio of areas = 90 cm^2 / 48 cm^2