two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the smaller roof is 4.5 feet, find the corresponding altitude of the larger roof. Round to the nearest hundredth.
A. 7.5
B. 6.75
C. 6
D. 4
4.5 : x = 2 : 3
4.5/x = 2/3
2x = 13.5
x = 6.75
To find the corresponding altitude of the larger roof, we need to use the concept of similarity and the given ratio between the corresponding sides.
In similar triangles, corresponding sides are in proportion. In this case, the ratio of the corresponding sides of the triangular roofs is given as 2:3. Since the altitude is a side of the triangle, it is also included in this ratio.
Let the altitude of the larger roof be x feet.
According to the given ratio, we can set up the following proportion:
(altitude of smaller roof) / (altitude of larger roof) = (corresponding sides of smaller roof) / (corresponding sides of larger roof)
4.5 / x = 2 / 3
To find x, we can cross-multiply and solve the resulting equation:
2x = 3 * 4.5
2x = 13.5
Dividing both sides by 2, we get:
x = 13.5 / 2
x = 6.75
Therefore, the corresponding altitude of the larger roof is 6.75 feet.
Rounded to the nearest hundredth, the answer is B. 6.75.