A rectangular tray is 30cm long, 20cm wide and 6cm high. A similar tray is 12cm long .what is the scale factor of the enlargement of the small tray to the bigger tray
First, we need to determine the dimensions of the bigger tray. Since the scale factor is the ratio of corresponding lengths in the two similar figures, we can use the length of the smaller tray and the length of the larger tray to find the scale factor.
Let x be the length of the larger tray. We know that the scale factor is given by:
scale factor = (length of larger tray) / (length of smaller tray)
scale factor = x / 12
We want to find x. To do this, we can use the fact that the two trays are similar, which means that the ratio of corresponding dimensions is constant. Specifically:
length ratio = (length of larger tray) / (length of smaller tray) = x / 12
width ratio = (width of larger tray) / (width of smaller tray) = ?
height ratio = (height of larger tray) / (height of smaller tray) = ?
We can use the length ratio to find the other ratios. Since the two trays are similar, the ratios should be the same for all dimensions:
length ratio = width ratio = height ratio
So we have:
x / 12 = 20 / ? (width ratio)
x / 12 = 6 / ? (height ratio)
To find the width ratio, we can cross-multiply and solve for ?:
x / 12 = 20 / ?
? = 20 * 12 / x
To find the height ratio, we can do the same:
x / 12 = 6 / ?
? = 6 * 12 / x
Now we substitute these ratios back into the length ratio and solve for x:
x / 12 = ? / ?
x / 12 = (20 * 12 / x) / (6 * 12 / x)
x / 12 = 20 / 6
x = 12 * (20 / 6)
x = 40
Therefore, the scale factor is:
scale factor = (length of larger tray) / (length of smaller tray) = 40 / 12 = 10 / 3
Alternatively, we could have used the width or height ratio to find x. For example, using the width ratio:
x / 12 = 20 / ?
x = 12 * (20 / 30)
x = 8
Then the length ratio gives the same scale factor:
scale factor = (length of larger tray) / (length of smaller tray) = 8 / 12 = 10 / 3
A rectangular tray is 30cm long, 20cm wide and 6cm high. A similar tray is 12cm long. What is the height of the smaller tray
We can use the fact that the two trays are similar, which means that the ratio of corresponding dimensions is constant. Specifically:
length ratio = (length of larger tray) / (length of smaller tray)
width ratio = (width of larger tray) / (width of smaller tray)
height ratio = (height of larger tray) / (height of smaller tray)
We can use any two of these ratios to find the third. For example, we can use the length and height ratios:
length ratio = (length of larger tray) / (length of smaller tray) = 30 / 12 = 5 / 2
height ratio = (height of larger tray) / (height of smaller tray)
We want to solve for the height of the smaller tray, so we rearrange the height ratio:
height ratio = (height of larger tray) / (height of smaller tray) = 1 / (height of smaller tray / height of larger tray)
We substitute the known length ratio and height ratio, and solve for the height of the smaller tray:
5 / 2 = 1 / (height of smaller tray / 6)
(height of smaller tray / 6) = 1 / (5 / 2)
(height of smaller tray / 6) = 2 / 5
height of smaller tray = (2 / 5) * 6
height of smaller tray = 2.4 cm
Therefore, the height of the smaller tray is 2.4 cm.
12cm and 50cm how will I put it in a fraction form
To put 12 cm and 50 cm in fractional form, we can write them with a common denominator, and then combine them into a single fraction:
12 cm = 120/10 cm (multiply by 10/10 to get a denominator of 10)
50 cm = 500/10 cm (multiply by 10/10 to get a denominator of 10)
Now we can combine them into a single fraction with a common denominator of 10:
120/10 cm + 500/10 cm = 620/10 cm
So, 12 cm and 50 cm can be expressed as the fraction 620/10 cm. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 10:
620/10 cm = (620/10) / (10/10) cm = 62/1 cm
Therefore, the fraction form of 12 cm and 50 cm is 62/1 cm.
To find the scale factor of the enlargement of the small tray to the bigger tray, we need to compare the corresponding lengths of the two trays.
The length of the small tray is 12cm, and the length of the bigger tray is 30cm. Therefore, the scale factor is calculated by dividing the length of the bigger tray by the length of the small tray:
Scale factor = Length of bigger tray / Length of smaller tray
Scale factor = 30cm / 12cm
Scale factor ≈ 2.5
Hence, the scale factor of the enlargement of the small tray to the bigger tray is approximately 2.5.
To find the scale factor between the small and big tray, we can compare the corresponding dimensions of the two trays.
The length of the small tray is 12cm, and the length of the big tray is 30cm.
So the scale factor of the enlargement of the small tray to the big tray is given by:
scale factor = length of big tray / length of small tray
scale factor = 30cm / 12cm
Simplifying this fraction, we get:
scale factor = 2.5
Therefore, the scale factor of the enlargement of the small tray to the big tray is 2.5.