Question

Can anyone help me with these two plz

Answer 1

Answer:

Part 1) The scale factor is $1.5$

Part 2) The altitude QS is $4\ units$

Part 3) The scale factor is $\frac{2}{3}$

Part 4) The value of x is $12\ units$

Part 5) The perimeter of ABCDE is $46\ units$

Step-by-step explanation:

Part 1) Find the scale factor of triangle TQR to triangle NQP

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z-----> the scale factor

$z=\frac{NP}{RT}$

substitute the values

$z=\frac{24}{16}=1.5$

Part 2) Find the length of the altitude QS

we know that

To find the altitude QS, divide the altitude of triangle NQP by the scale factor

so

$QS=\frac{6}{1.5}=4\ units$

Part 3) Find the scale factor of FGHJK to ABCDE

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z-----> the scale factor

$z=\frac{AB}{FG}$

substitute the values

$z=\frac{10}{15}=\frac{2}{3}$

Part 4) Find the value of x

we know that

The value of x is equal to multiply the length side FK by the scale factor

so

$AE=FK(z)$

substitute the values

$AE=18(2/3)=12\ units$

Part 5) Find the perimeter of ABCDE

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of ABCDE

y-----> the perimeter of FGHJK

$z=\frac{x}{y}$

we have

$z=\frac{2}{3}$

$y=15+9+12+15+18=69\ units$

substitute the values

$z=\frac{x}{y}$

$x=(z)(y)=\frac{2}{3}(69)=46\ units$