A certain tree casts a shadow 6 m long. At the same time, a nearby man measuring 2 m tall casts a shadow 4 m long. What is the height of the tree?
We can set up a proportion to solve this problem. Let the height of the tree be represented by "h". Thus, we can write the proportion as:
(2 m) / (4 m) = h / (6 m)
Cross-multiplying, we get:
2 * 6 = 4 * h
12 = 4h
Dividing both sides by 4, we find:
h = 12 / 4 = 3
Therefore, the height of the tree is 3 meters.
We can set up a proportion to solve this problem. Let the length of the shadow of the building be represented by "x". Thus, we can write the proportion as:
5 ft / 3 ft = 30 ft / x
Cross-multiplying, we get:
5 ft * x = 3 ft * 30 ft
5x = 90 ft
Dividing both sides by 5, we find:
x = 90 ft / 5 = 18 ft
Therefore, the length of the shadow of the building is 18 feet.
Since the two triangles are similar, their corresponding sides are proportional. We can write the ratio of corresponding sides as:
(side of larger triangle) / (side of smaller triangle) = (perimeter of larger triangle) / (perimeter of smaller triangle)
Let's use "x" to represent the length of the shortest side of the larger triangle. The perimeter of the smaller triangle is 6 in + 7 in + 12 in = 25 in. Plugging in all the values, we have:
(x) / (6 in) = (75 in) / (25 in)
Cross-multiplying, we get:
25x = 6 in * 75 in
25x = 450 in
Dividing both sides by 25, we find:
x = 450 in / 25 = 18 in
Therefore, the length of the shortest side of the larger triangle is 18 inches.
A person 5 ft. tall is standing near a building 30 ft. high. If the length of the person’s shadow is 3 ft., what is the length of the shadow of the building?
Two triangles used in an art project are similar. The sides of the smaller triangle have lengths of 6 in., 7 in., and 12 in. The perimeter of the larger triangle is 75 in. What is the length of the shortest side of the larger triangle?
Three sides of a triangle measure 3, 4, and 5. Solve for the length of the shortest side of a similar triangle whose longest side has a length of 20.
Since the two triangles are similar, their corresponding sides are proportional. We can write the ratio of corresponding sides as:
(shortest side of larger triangle) / (shortest side of smaller triangle) = (longest side of larger triangle) / (longest side of smaller triangle)
Let's use "x" to represent the length of the shortest side of the smaller triangle. The longest side of the larger triangle is 20. Plugging in all the values, we have:
(x) / (3) = (20) / (5)
Cross-multiplying, we get:
5x = 3 * 20
5x = 60
Dividing both sides by 5, we find:
x = 60 / 5 = 12
Therefore, the length of the shortest side of the smaller triangle is 12.