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In the sunlight, a cactus casts a 9 ft shadow. At the same time an oversized groundhog 6 ft tall casts a 4 ft shadow. Use similar triangles to find the height of the cactus. a. 11.69 ft c. 13.5 ft b. 10.53 ft d. 10.2 ft

Respuesta :

6/4 = x/9 
x = 6.9 / 4 
x = 27 / 2 = 13,5 

6/4 is the ratio of the grounding's actual height to its shadow's length. Since the shadow must have the same ratio for the cactus as well, we input the shadow's length and we put an x for the part we do not know (the actual length.) Then we use basic algebra to solve.
isyllus

Answer:

The height of the cactus is 13.5 ft.

C is correct.

Step-by-step explanation:

In the sunlight, a cactus casts a 9 ft shadow.

At the same time an oversized groundhog 6 ft tall casts a 4 ft shadow.

Ratio of shadow to height is same for all at same time.

Ratio of groudhog [tex]=\frac{4}{6}[/tex]

Let the height of the cactus be x ft

Ratio of cactus [tex]=\dfrac{9}{x}[/tex]

Both ratio must be equation because similar triangle theorem, Ratio of two sides is equal.

Therefore,

[tex]\frac{4}{6}=\dfrac{9}{x}[/tex]

Now we solve for x

[tex]4x=6\times 9[/tex]

[tex]x=13.5[/tex] ft

Hence, The height of the cactus is 13.5 ft.

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