In the diagram, ∆PQR ~ ∆QRS. Which pair of equations will help you find the value of x?
x/5 = 13/RS x² + RS² = 13²
5/13 = 13/RS x² + 13² = RS²
x/13 = 13/5 x² + RS² = 13²
13/5 = 13/RS x² + 13² = RS²
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In the diagram, ∆PQR ~ ∆QRS. Which pair of equations will help you find the value of x?
x/5 = 13/RS x² + RS² = 13²
5/13 = 13/RS x² + 13² = RS²
x/13 = 13/5 x² + RS² = 13²
13/5 = 13/RS x² + 13² = RS²
To solve for the value of ( x ) given that ( Delta PQR sim Delta QRS ), we can use the property of similar triangles, which states that the ratios of corresponding sides are equal.
For the triangles ( Delta PQR ) and ( Delta QRS ), corresponding sides would give us the equation:
[
frac{x}{5} = frac{13}{RS}
]
This is derived from the corresponding sides ( PQ ) and ( QR ) compared to ( QR ) and ( RS ).
Therefore, the correct choice is:
x/5 = 13/RS
This equation will help us set up the proportions needed to solve for ( x ) given ( RS ).
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