Question

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Answer 1

Answer:

1. x = 4

2. x = 20

Step-by-step explanation:

1.

ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:

$\dfrac{AC}{AJ}=\dfrac{AB}{AK}$

We have:

AC = 1 + 4 = 5

AJ = 1

AB = 1 + x

AK = 1

Substitute:

$\dfrac{5}{1}=\dfrac{1+x}{1}$

$5=1+x$           subtract 1 from both sides

$4=x\to x=4$

2.

ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:

$\dfrac{VU}{VM}=\dfrac{VT}{VN}$

We hve:

VU = x + 8

VM = x

VT = 49

VN = 49 - 14 = 35

Substitute:

$\dfrac{x+8}{x}=\dfrac{49}{35}$              cross multiply

$35(x+8)=49x$          use the distributive property a(c + b) = ab + ac

$35x+280=49x$              subtract 35x from both sides

$280=14x$         divide both sides by 14

$20=x\to x=20$