Question

1. $delta cde sim delta fge$, find $ce$8. $delta kmz sim delta kdh$, find $x$9. $delta agn sim delta fls$, find $x$10. $delta cse sim delta yje$, find $ey$11. if $delta klm sim delta pqr$ with a scale factor of $3:5$, find the perimeter of $delta pqr$.12. if $delta tsr sim delta tfe$, find the perimeter of $delta tfe$.

Explanation:

Problem 8:

Step1: Set up proportion

$\frac{x+8}{21} = \frac{32}{28}$

Step2: Simplify right-hand side

$\frac{32}{28} = \frac{8}{7}$

Step3: Solve for $x$

$7(x+8) = 8 \times 21$
$7x + 56 = 168$
$7x = 112$
$x = 16$

Problem 10:

Step1: Set up proportion

$\frac{18}{10} = \frac{x-2}{x+1}$

Step2: Cross-multiply to solve

$18(x+1) = 10(x-2)$
$18x + 18 = 10x - 20$
$8x = -38$
$x = -\frac{19}{4}$

Step3: Calculate $EY$

$EY = x+1 = -\frac{19}{4} + 1 = -\frac{15}{4}$ (Note: Negative length indicates direction; magnitude is $\frac{15}{4}$)

Problem 11:

Step1: Find perimeter of $\Delta KLM$

$6 + 12 + 15 = 33$

Step2: Use scale factor to find $\Delta PQR$ perimeter

Let $P_{PQR}$ = perimeter of $\Delta PQR$. Scale factor $\frac{3}{5} = \frac{P_{KLM}}{P_{PQR}}$
$P_{PQR} = 33 \times \frac{5}{3} = 55$

Problem 12:

Step1: Find scale factor

$\frac{40}{25} = \frac{8}{5}$

Step2: Find perimeter of $\Delta TSR$

$40 + 54 + 22 = 116$

Step3: Calculate perimeter of $\Delta TFE$

Let $P_{TFE}$ = perimeter of $\Delta TFE$. $\frac{P_{TSR}}{P_{TFE}} = \frac{8}{5}$
$P_{TFE} = 116 \times \frac{5}{8} = 72.5$

Answer:

1. $x=16$
2. $x=9$ (already solved correctly)
3. $EY=-\frac{15}{4}$ (or $\frac{15}{4}$ for magnitude)
4. Perimeter of $\Delta PQR$ is 55
5. Perimeter of $\Delta TFE$ is 72.5