Answer:
p = 16
Step-by-step explanation:
Given that ∆FGH is similar to ∆DEF, it follows that the ratio of their corresponding side lengths would be equal. Therefore:
[tex] \frac{FH}{DF} = \frac{FG}{DE} [/tex]
FH = 12
DF = p
FG = 24
DE = 32
Plug in the values
[tex] \frac{12}{p} = \frac{24}{32} [/tex]
Cross multiply
[tex] 12*32 = 24*p [/tex]
[tex] 384 = 24p [/tex]
Divide both sides by 24
[tex] \frac{384}{24} = \frac{24p}{24} [/tex]
[tex] 16 = p [/tex]
p = 16
