Question

The areas of two similar squares are 16m2 and 49m2 what is the scale factor of their side lengths

Answer 1

Answer: 4/7 is the right answer on Acellus

Explanation:

Answer 2

Given:

The areas of two similar squares are 16m² and 49m².

To find:

The scale factor of their side lengths.

Solution:

We know that the ratio of the areas of the similar squares is proportional to the ratio of square of there sides.

`\frac{\text{Area of first square}}{\text{Area of second square}}=\frac{(\text{Side length of first square})^2}{(\text{Side length of second square})^2}`

`(16\ m^2)/(49\ m^2)=(s_1^2)/(s_2^2)`

`(4^2)/(7^2)=\left((s_1)/(s_2)\right)^2`

`\left((4)/(7)\right)^2=\left((s_1)/(s_2)\right)^2`

Taking square root on both sides, we get

`(4)/(7)=(s_1)/(s_2)`

`(s_1)/(s_2)=(4)/(7)`

Now, the scale factor is the ratio of side length of second square to the side length of first square.

`k=(s_2)/(s_1)`

`k=(7)/(4)`

Therefore, the scale factor of their side lengths is
`k=(7)/(4)`.