Home » Past Questions » Mathematics » In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the...

In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the...


Question

In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the value of x.

Options

A) 5.6

B) 6.5

C) 6.6

D) 6.8

The correct answer is A.

Explanation:

\(\frac{/PS/}{/PQ/} = \frac{/PT/}{/PR/}\)

\(\frac{x}{4 + x} = \frac{7}{7 + 5}\)

\(\frac{x}{4 + x} = \frac{7}{12}\)

(2x = 7)(4 + x); 12x = 28 + 7x

12x - 7x = 28

5x = 28

x = \(\frac{28}{5}\)

x = 5.6


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Dicussion (1)

  • \(\frac{/PS/}{/PQ/} = \frac{/PT/}{/PR/}\)

    \(\frac{x}{4 + x} = \frac{7}{7 + 5}\)

    \(\frac{x}{4 + x} = \frac{7}{12}\)

    (2x = 7)(4 + x); 12x = 28 + 7x

    12x - 7x = 28

    5x = 28

    x = \(\frac{28}{5}\)

    x = 5.6

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