Question

Please help, I don’t understand any of this.

Answer 1

The scale factor is 9. The values of x, y, and z are 91, 45, and 72, respectively. The perimeters of the two quadrilaterals are 110 and 990, respectively. The ratio of the perimeters is 1:9.

Question 11:

To find the scale factor, we can compare the lengths of any two corresponding sides.

For example, we can compare the lengths of sides
`\overline{AB}$ and $\overline{EF}$`.

Scale factor =
`\frac{\text{Length of side in larger figure}}{\text{Length of side in smaller figure}}`

Scale factor =
`(91)/(21)$ = **4.5**`

Question 12:

To find the values of
`$x$`,
`$y$`, and
`$z$`, we can use the fact that corresponding sides of similar figures are proportional.

For example, we can write the following proportion:

`(x)/(20) = (45)/(63)`

Multiplying both sides by $20$, we get:

`x = (20 \cdot 45)/(63) = 30`

Similarly, we can write the following proportion:

`(y)/(10) = (72)/(63)`

Multiplying both sides by $10$, we get:

`y = (10 \cdot 72)/(63) = 12`

Finally, we can find the value of
`$z$` using the fact that the angles in a quadrilateral add up to
`$360^\circ$`.

`360^\circ = 63^\circ + 72^\circ + 45^\circ + z`

Subtracting the other angles, we get:

`z = 360^\circ - 63^\circ - 72^\circ - 45^\circ = 180^\circ`

Therefore, the values of
`$x$`,
`$y$`, and
`$z$` are
`**$30$, $12$, and $180$**`, respectively.

Question 13:

To find the perimeter of each quadrilateral, we can add up the lengths of all the sides.

For quadrilateral ABCD, the perimeter is:

Perimeter of ABCD = 21 + 20 + 91 + 10 = 142

For quadrilateral EFGH, the perimeter is:

Perimeter of EFGH = 45 + 30 + 72 + 12 = 159

Question 14:

To find the ratio of the perimeters, we can divide the perimeter of the larger quadrilateral by the perimeter of the smaller quadrilateral.

Ratio of perimeters =
`(159)/(142) = \boxed{(90)/(81)}`