The sides of two similar pentagons are in a ratio of 2 : 7. The area of the larger pentagon is 112 in2 . Find the area of the smaller pentagon.Question 5Select one:a.17.5 in2b.9.14 in2c.91.4 in2d.1.75 in2
Question
The sides of two similar pentagons are in a ratio of 2 : 7. The area of the larger pentagon is 112 in2 . Find the area of the smaller pentagon.Question 5Select one:a.17.5 in2b.9.14 in2c.91.4 in2d.1.75 in2
Solution
The areas of similar figures are proportional to the square of the ratio of their corresponding sides.
Given that the ratio of the sides of the two pentagons is 2:7, the ratio of their areas will be (2^2) : (7^2) = 4 : 49.
We know that the area of the larger pentagon is 112 in^2.
Let's denote the area of the smaller pentagon as x.
So, we can set up the proportion:
4/49 = x/112
To solve for x, cross-multiply:
4 * 112 = 49 * x
448 = 49x
To isolate x, divide both sides by 49:
x = 448 / 49
x = 9.14 in^2
So, the area of the smaller pentagon is 9.14 in^2.
Therefore, the correct answer is b. 9.14 in^2.
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