Using the leg rule, the length of PS is: A. 6√12.
The leg rule is given as: hypotenuse/leg = leg/part.
Given triangle PQS, thus:
Leg = PS = ?
Hypotenuse = RS + QR = 18 + 6 = 24
Part = RS = 18
Plug in the values into the leg rule:
24/PS = PS/18
Cross multiply
(PS)(PS) = (24)(18)
PS² = 432
PS = √432
PS = √(36 × 12)
PS = 6√12
Therefore, using the leg rule, the length of PS is: A. 6√12.
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Answer:
PS=12√3
Step-by-step explanation:
The lengths of the two segments of the hypotenuse formed by the altitude are given.
By the Similarity in Right Triangles Theorem, △SPQ ~△SRP.
To find the value of PS, set up a proportion using ratios involving PS
and the known side in two of the similar triangles.
PS/QS=RS/PS
Cross multiply.
PS^2=QS⋅RS
Substitute the given lengths into the equation, considering that QS=RS+QR
PS^2=(18+6)⋅18
Simplify.
PS^2=24⋅18
Find the positive square root.
PS=√24⋅18
Factor the terms inside the square root.
PS=√2⋅2⋅2⋅3⋅2⋅3⋅3
PS=√2^4−−√3^2−−√3–√
Simplify.
PS=4⋅3√3
Simplify again.
PS=12√3
Therefore, the length of PS¯¯¯¯¯ is 12√3.
