In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the value of x
Attached Figure / Diagram
A
5.6
B
6.5
C
6.6
D
6.8
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{/PS/}{/PQ/} = \frac{/PT/}{/PR/}\)
\(\frac{x}{4 + x} = \frac{7}{7 + 5}\)
\(\frac{x}{4 + x} = \frac{7}{12}\)
(2x = 7)(4 + x); 12x = 28 + 7x
12x - 7x = 28
5x = 28
x = \(\frac{28}{5}\)
x = 5.6
Source: Myschool Past Questions Archive (Record #36491)