Q:

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x. What is the value of x? 12 units 15 units 20 units 24 units

Accepted Solution

A:
Answer:Option B.Step-by-step explanation:It is given that ΔSRQ is a right angle triangle, ∠SRQ is right angle.RT is altitude on side SQ, ST=9, TQ=16 and SR=x.In ΔSRQ and ΔSTR,[tex]m\angle S=m\angle S[/tex]           (Reflexive property)[tex]m\angle R=m\angle T[/tex]           (Right angle)By AA property of similarity,[tex]\triangle SRQ\sim \triangle STR[/tex]Corresponding parts of similar triangles are proportional.[tex]\dfrac{SR}{SQ}=\dfrac{ST}{SR}[/tex]Substitute the given values.[tex]\dfrac{x}{9+16}=\dfrac{9}{x}[/tex][tex]\dfrac{x}{25}=\dfrac{9}{x}[/tex]On cross multiplication we get[tex]x^2=25\times 9[/tex][tex]x^2=225[/tex]Taking square root on both sides.[tex]x=\sqrt{225}[/tex][tex]x=15[/tex]The value of x is 15. Therefore, the correct option is B.