Question

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.

Answer 1

Answer:

the answer is 9

Step-by-step explanation:

Just did the lesson

Answer 2

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.