A triangle has an area of 20 inches squared. Every dimension of the triangle is multiplied by a scale factor, and the new triangle has an area of 180 inches squared. What is the scale factor.
if a rectangle (or any 2-dimensional figure) is scaled by a factor of n, then
length l becomes nl
width w becomes nw
area lw becomes (nl)(nw) = n^2(lw) = n^2 times the old area
For your rectangle, the new area is 9 times the old area, so the scale factor is √9 = 3
Dsad
A triangle has an factors of 20in every dimension
To find the scale factor, we need to compare the areas of the two triangles.
The area of the first triangle is given as 20 inches squared.
Let's assume the scale factor is 'x'. This means that every dimension of the triangle is multiplied by 'x' to get the dimensions of the new triangle.
The area of the new triangle is given as 180 inches squared.
So, if every dimension of the original triangle is multiplied by 'x' to get the dimensions of the new triangle, the relationship between their areas can be expressed as:
(x * original area) = new area
(x * 20) = 180
To find the value of 'x', we can rearrange the equation:
x = new area / original area
x = 180 / 20
x = 9
Therefore, the scale factor is 9.