the ratio of the area of a smaller triangle to the area of a larger triangle is 1:4. if the are of the smaller triangle is 30, find the area of the larger triangle.
1:4 = 30:A
or,
1/4 = 30/A
or
4 = A/30
A = 120
To find the area of the larger triangle, we need to first determine the area of the smaller triangle. In this case, we are given that the area of the smaller triangle is 30.
Since we are given that the ratio of the area of the smaller triangle to the area of the larger triangle is 1:4, we can set up the equation:
(area of smaller triangle) / (area of larger triangle) = 1 / 4
Substituting the given values:
30 / (area of larger triangle) = 1 / 4
To solve for the area of the larger triangle, we can cross-multiply:
30 * 4 = 1 * (area of larger triangle)
120 = area of larger triangle
Therefore, the area of the larger triangle is 120.