Question

Find x and y 30 points

Answer 1

Since the two triangles are similar

$\frac{5 + x}{5} = \frac{7 + y}{7} = \frac{10}{8} \\ \implies \frac{5 + x}{5} = \frac{10}{8} \\ \implies x = \frac{50}{8} - 5 = \frac{50 - 40}{8} = \frac{10}{8} = \frac{5}{4} \\ \therefore x = \frac{5}{4}$

Also,

$\\ \frac{7 + y}{7} = \frac{10}{8} \\ \implies y = \frac{70}{8} - 7 = \frac{70 - 56}{8} \\ \therefore y = \frac{14}{8} = \frac{7}{4}$

Answer 2

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