A painter needs to know the height of a building to estimate the amount of paint needed for the front side. When the building cast an 18 ft shadow, the 6 ft tall painter casts a 3 ft long shadow. How tall is the building?
Would it be 36 ft?
Right.
To solve this problem, we can use similar triangles. The height of the building and the height of the painter form one pair of corresponding sides of similar triangles, and the lengths of their shadows form another pair of corresponding sides.
Let's define the variables:
h = height of the building
s = length of the shadow of the building
p = height of the painter
q = length of the shadow of the painter
According to the problem, we have:
s = 18 ft
p = 6 ft
q = 3 ft
Using the concept of similar triangles, we can set up the proportion:
h/s = p/q
Plugging in the given values, we get:
h/18 = 6/3
Now we can solve for h:
h = (18 * 6) / 3
h = 36 ft
So, the height of the building is 36 ft.
To determine the height of the building, we can use the concept of proportions.
Let the height of the building be "x" feet. According to the given information, the ratio of the height of the building to the length of its shadow is the same as the ratio of the painter's height to the length of his shadow.
So, we can set up the proportion:
x / 18 = 6 / 3
Now, we can cross-multiply and solve for x:
3x = 18 * 6
3x = 108
x = 108 / 3
x = 36
Therefore, the height of the building is 36 feet.