Question

Given CS = 3, SB = 6, CR = 4, and RA = x. What must the value of x be in order to prove SR || BA? Justify your answer.

Answer 1

Answer:

x = 8

Step-by-step explanation:

Given that CS = 3, SB = 6

=> BC = CS + SB = 3 + 6 = 9

Given that CR = 4 and RA = x.

=> AC = CR + RA = 4 + x

In triangle ACB, according to the Thales theorem, if SR is parallel with BA the rate of (CS/BC) is equal to the rate of (RC/AC).

⇔ CS/ BC = RC/ AC

⇔ 3/ 9 = 4/(4+x)

⇔ 3 × (4 + x) = 4 × 9

⇔ 12 + 3x = 36

⇔ 3x = 36 - 12 = 24

⇔ x = 24÷3 = 8

So that x =8, SR is parallel with BA

Answer 2

Answer:

See below

Step-by-step explanation:

Since the triangles appear to be similar, let's set up a proportion and get what the value of x must be for the triangles to be similar.

CS/CR = CB/CA

3/4 = 9/c

3c = 36

CA equals 12

Now, if we subtract the value of CR, since AB + BC = AC, we will have the value of RA and the value x.

12 - 4 = 8

X must equal 8 for the triangles to be similar.

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