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Sagot :
Since the two triangles are similar
[tex] \frac{5 + x}{5} = \frac{7 + y}{7} = \frac{10}{8} \\ \implies \frac{5 + x}{5} = \frac{10}{8} \\ \implies x = \frac{50}{8} - 5 = \frac{50 - 40}{8} = \frac{10}{8} = \frac{5}{4} \\ \therefore x = \frac{5}{4} [/tex]
Also,
[tex] \\ \frac{7 + y}{7} = \frac{10}{8} \\ \implies y = \frac{70}{8} - 7 = \frac{70 - 56}{8} \\ \therefore y = \frac{14}{8} = \frac{7}{4} [/tex]
Answer:
Scalar factor (k) = Image/Object = 10/8 = 5/4
Also Scalar factor = (5 + x)/5
5/4 = (5 + x)/5
multiplying both sides by 20 gives;
5 × 5 = 4(5 + x)
25 = 20 + 4x
4x = 25 - 20
x = 5/4
Scalar factor = (7 + y)/7
5/4 = (7 + y)/7
multiplying both sides by 28 gives;
7 × 5 = 4(7 + y)
35 = 28 + 4y
4y = 35 - 28
y = 7/4
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