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Viktor [21]
3 years ago
6

The sides of a quadrilateral are 3, 4, 5, and 6. Find the length of the shortest side of a similar quadrilateral whose area is 9

times as great.
Mathematics
2 answers:
Digiron [165]3 years ago
7 0

Answer:

the answer is 9

Step-by-step explanation:

Just did the lesson

Georgia [21]3 years ago
4 0

Answer:

9 units.

Step-by-step explanation:

Let us assume that length of smaller side is x.

We have been given that the sides of a quadrilateral are 3, 4, 5, and 6. We are asked to find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.

We know that sides of similar figures are proportional. When the proportion of  similar sides of two similar figures is \frac{m}{n}, then the proportion of their area is \frac{m^2}{n^2}.

We can see that length of smaller side of 1st quadrilateral is 3 units, so we can set a proportion as:

\frac{x^2}{3^2}=\frac{9}{1}

\frac{x^2}{9}=\frac{9}{1}

x^2=9\cdot 9

x^2=81

Take positive square root as length cannot be negative:

\sqrt{x^2}=\sqrt{81}

x=9

Therefore, the length of the shortest side of the similar quadrilateral would be 9 units.

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