Jack is 1.75 m tall and casts a shadow 2.25 m long. At the same time, a statue casts a shadow 9 m long. What is the height of the statue?
A.
11.6 m
B.
7 m
C.
5.75 m
D.
4 m
We can use proportions to solve this problem. Let x be the height of the statue.
Then, we can set up the proportion:
(1.75 m) / (2.25 m) = x / (9 m)
To solve for x, we can cross multiply and then solve for x:
(1.75 m)(9 m) = (2.25 m)(x)
15.75 m^2 = 2.25 m*x
Now, divide both sides by 2.25 m to solve for x:
15.75 m^2 / 2.25 m = x
7 m = x
Therefore, the height of the statue is 7 m.
The answer is (B) 7 m.
To find the height of the statue, we can set up a proportion between the height of Jack and the length of his shadow, and the height of the statue and the length of its shadow.
Let's define:
h = height of the statue
x = length of the shadow of the statue
The proportion can be set up as:
1.75 m / 2.25 m = h / 9 m
To solve for h, we can cross multiply and then divide:
1.75 m * 9 m = 2.25 m * h
15.75 m^2 = 2.25 m * h
Now, divide both sides of the equation by 2.25 m:
15.75 m^2 / 2.25 m = h
7 m = h
Therefore, the height of the statue is 7 m.
Therefore, the answer is B. 7 m.
To find the height of the statue, we can use a proportion based on the similar triangles formed by Jack and his shadow, and the statue and its shadow.
Let's denote the height of the statue as "x".
The proportion can be set up as follows:
(Jack's height)/(Jack's shadow) = (Statue's height)/(Statue's shadow)
Substituting the given values:
1.75 m / 2.25 m = x / 9 m
Now we can solve for "x" by cross-multiplying and then dividing:
1.75 m * 9 m = x * 2.25 m
15.75 m = 2.25x
x = 15.75 m / 2.25
x = 7 m
Therefore, the height of the statue is 7 m. The correct option is B.