can you please solve this
Answers
Answer:
Step-by-step explanation:
Given that:
In triangle PQR, PS is perpendicular to QR. find the sides marked a and b. if PR=41, QS=12 and SR=40
To find: a and b
Solution:
In ∆PQR,
As PS is perpendicular.
∆PSR is right angle triangle,right angle at S
here Base(SR)=40 cm
Hypotenuse(PR)=41 cm
Perpendicular(PS)=a=?
To find PS,apply Pythagoras theorem in ∆PSR
\begin{gathered}( {PR)}^{2} = ( {SR)}^{2} + ( {PS)}^{2} \\ \\ ( {41)}^{2} = ( {40)}^{2} + {a}^{2} \\ \\ {a}^{2} = 1681 - 1600 \\ \\ {a}^{2} = 81 \\ \\ \bold{\red{a = 9} }\\ \\ \end{gathered}
(PR)
2
=(SR)
2
+(PS)
2
(41)
2
=(40)
2
+a
2
a
2
=1681−1600
a
2
=81
a=9
Thus,
PS= a= 9cm
Now,
∆PSQ is right angle triangle,right angle at S
here Base(SQ)=12 cm
Hypotenuse(QP)=b=?
Perpendicular(PS)=9 cm
Apply Pythagoras theorem in ∆PSQ
\begin{gathered}( {QP)}^{2} = ( {SQ)}^{2} + ( {PS)}^{2} \\ \\ ( {QP)}^{2} = {b}^{2} = ( {12)}^{2} + ( {9)}^{2} \\ \\ {b}^{2} = 144 + 81 \\ \\ {b}^{2} = 225 \\ \\ b = \sqrt{225} \\ \\ \bold{\green{b = 15}} \\ \\ \end{gathered}
(QP)
2
=(SQ)
2
+(PS)
2
(QP)
2
=b
2
=(12)
2
+(9)
2
b
2
=144+81
b
2
=225
b=
225
b=15
Thus,
b= 15 cm.
Final Answer: a= 9 cm,b= 15 cm
Hope it helps you.
Step-by-step explanation:
- please make it a brainliest answer.
Answer:
The word democracy comes from the Greek words "demos", meaning people, and "kratos" meaning power; so dem
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