The surface areas of two similar solids are 36sq. yds and 144 sq yds. Find the ratio of their linear measures.
That would be the square root of the area ratio.
Sqrt(144/36) = sqrt4 = 2
To find the ratio of the linear measures of two similar solids, we need to compare their surface areas.
Let's assume the linear measure of the first solid is 'x' and the linear measure of the second solid is 'y'.
The surface area of a solid directly depends on the square of its linear measure. So, the ratio of the surface areas (A) of two similar solids is given by (A1/A2) = (x^2/y^2).
In this case, the surface areas given are 36 sq. yds and 144 sq. yds. So, we have (36/144) = (x^2/y^2).
To simplify the equation, we can cross multiply and rewrite as (36 * y^2) = (144 * x^2).
Now, let's solve for 'x' in terms of 'y' by dividing both sides of the equation by 144 and then taking the square root:
(36 * y^2)/144 = (144 * x^2)/144
(y^2)/4 = x^2
x = √(y^2/4)
x = y/2
Therefore, the linear measure ratio (x/y) is 1/2.
The ratio of their linear measures is 1:2.