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Sagot :
Hence the area of the second rhombus is 45 square meters
The area of a rhombus is expressed as
A = base * height
For the rhombus with an area of 5 square meters and a side length of 3 meters
Height = Area/length
Height = 5/3 metres
Since the length of a similar rhombus is 9meters, the scale factor will be expressed as;
k = ratio of the lengths = 9/3
k = 3
Height of the second rhombus = 3 * height of the first rhombus
Height of the second rhombus = 3 * 5/3
Height of the second rhombus = 5 meters
Area of the second rhombus = length * height
Area of the second rhombus = 5 * 9
Area of the second rhombus = 45 square meters
Hence the area of the second rhombus is 45 square meters
Learn more here: brainly.com/question/20247331
The correct option is option B;
(B) 45 square meters
The known parameters in the question are;
The area of the rhombus, A₁ = 5 m²
The length of one of the sides of the rhombus, a = 3 m
The length of a side in a similar rhombus, b = 9 m
The unknown parameter;
The area of the second rhombus
Strategy or method;
We have that two shapes are similar if their corresponding sides are proportional
From the above statement we get that the ratio of the areas of the two shapes is equal to the square of the ratio of the lengths of the corresponding sides of the two shapes of follows;
[tex]\begin{array}{ccc}Length \ Ratio&&Area \ Ratio\\\dfrac{a}{b} &&\left (\dfrac{a}{b} \right)^2 \\&&\end{array}[/tex]
Let the area of the second rhombus be A₂, we get;
[tex]Area \ ratio = \dfrac{A_1}{A_2} = \left( \dfrac{a}{b} \right)^2[/tex]
Where;
a = 3 m, b = 9 m, and A₁ = 5 m², we get;
[tex]Area \ ratio = \dfrac{5 \ m^2}{A_2} = \left( \dfrac{3 \, m}{9 \, m} \right)^2 = \dfrac{1}{9}[/tex]
Therefore;
9 × 5 m² = A₂ × 1
A₂ = 45 m²
The area of the second rhombus, A₂ = 5 m².
Learn more about scale factors here;
https://brainly.com/question/20247331
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