Respuesta :
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 [tex]\frac{m}{n}[/tex], then the proportion of their area is [tex]\frac{m^2}{n^2}[/tex].
We can see that length of smaller side of 1st quadrilateral is 3 units, so we can set a proportion as:
[tex]\frac{x^2}{3^2}=\frac{9}{1}[/tex]
[tex]\frac{x^2}{9}=\frac{9}{1}[/tex]
[tex]x^2=9\cdot 9[/tex]
[tex]x^2=81[/tex]
Take positive square root as length cannot be negative:
[tex]\sqrt{x^2}=\sqrt{81}[/tex]
[tex]x=9[/tex]
Therefore, the length of the shortest side of the similar quadrilateral would be 9 units.
Answer:
the answer is 9
Step-by-step explanation:
Just did the lesson
