Answer:
B
Step-by-step explanation:
The height to height ratio of the 2 rectangles = 21 : 7 = 3 : 1, that is
The sides of the red rectangle are one third of the corresponding sides in the blue rectangle, thus
w = 34 ÷ 3 ≈ 11.33 ( to 2 dec. places ) → B
The value of w which represents the width of the smaller rectangle for this case is given by: Option B: 11.33 approx.
Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
We're specified that:
The two rectangles below have the same height-to-width ratio
[tex]H:W = \dfrac{H}{W} = \dfrac{21}{34}[/tex]
[tex]H:W = \dfrac{H}{W} = \dfrac{7}{w}[/tex]
They are equal, therefore, we get:
[tex]\dfrac{7}{w} = \dfrac{21}{34}\\\\\text{Multiplying } 34\times w\text{ on both the sides}\\\\7 \times 34 = 21 \times w\\\\\text{Dividing both the sides by 21 so as to get w on one side and rest on other}\\\\\dfrac{34}{3} = w\\\\w = \dfrac{34}{3} \approx 11.33 \: \rm units[/tex]
Thus, the value of w which represents the width of the smaller rectangle for this case is given by: Option B: 11.33 approx.
Learn more about ratio here:
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