A mirror 50cm height has on area of 100cm² you another mirror is twice as high h find the area scale factor find the area of the larger mirror
since area = length * height,
twice the height means twice the area
Now, if the mirror is circular, then twice the height means twice the radius
pi(2r)^2 = 4(pi r^2)
area grows as the square of the scale factor for similar shapes.
I want solution
To find the area scale factor, we need to compare the ratio of the areas of the two mirrors. Let's denote the height of the smaller mirror as h.
Area of smaller mirror = 100 cm²
Height of smaller mirror = 50 cm
Area of larger mirror = ?
Height of larger mirror = 2h (twice as high as the smaller mirror)
The area scale factor can be calculated using the formula:
Area scale factor = (Area of larger mirror) / (Area of smaller mirror)
First, let's find the area scale factor:
Area scale factor = (Area of larger mirror) / (Area of smaller mirror)
Area scale factor = (Area of larger mirror) / 100 cm²
Since the height of the larger mirror is twice the height of the smaller mirror, we can write:
Height of larger mirror = 2 * Height of smaller mirror
2h = 2 * 50 cm
2h = 100 cm
Now, let's find the area of the larger mirror:
Area of larger mirror = (Area scale factor) * (Area of smaller mirror)
Area of larger mirror = (2h / 100 cm²) * 100 cm²
Simplifying, we have:
Area of larger mirror = 2h
Therefore, the area scale factor is 2, and the area of the larger mirror is 2h.
To find the area scale factor, we need to compare the areas of the two mirrors. Let's call the height of the first mirror "h1" (which is 50 cm) and the height of the second mirror "h2" (which is twice as high as the first mirror, so it's 2 * h1).
The area of a mirror can be calculated by multiplying the height (h) by the width (w). However, since the mirrors are assumed to be rectangular, and we are only given the height, we can assume that the width is equal to the height.
So, the area of the first mirror (A1) is equal to h1 * h1, which is 50 cm * 50 cm = 2500 cm².
The area of the second mirror (A2) is equal to h2 * h2, which is (2 * h1) * (2 * h1) = 4 * h1 * h1 = 4 * 2500 cm² = 10,000 cm².
Now, to find the area scale factor, we divide the larger area by the smaller area: A2 / A1 = 10,000 cm² / 2500 cm² = 4.
So, the area scale factor is 4, which means the larger mirror has an area that is four times greater than the smaller mirror.
Therefore, the area of the larger mirror is 10,000 cm².