pair of positive number who sum is -5
Answers
Answer:
Answer :
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Length of side QR of ∆PQR is 5.5 cm.
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Explanation :
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Given :
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Area of two similar triangles, ∆ABC and ∆PQR are 100 cm² and 121 cm² respectively and length side BC of ∆ABC is 5 cm.
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To Find :
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Length of QR of ∆PQR?
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Solution :
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We are given that ∆ABC ∼ ∆PQR.
We clearly know that, if two triangles are similar the ratio of their area is proportional to square of ratio of their corresponding sides.
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Therefore,
\begin{gathered}\\ :\implies\:\sf \Bigg\{\dfrac{ar\big(\triangle{ABC}\big)}{ar\big(\triangle{PQR}\big)}\Bigg\} = {\Bigg\{\dfrac{BC}{QR}\Bigg\}}^{2}\end{gathered}
:⟹{
ar(△PQR)
ar(△ABC)
}={
QR
BC
}
2
\begin{gathered}\\ :\implies\:\sf \dfrac{100}{121} = \dfrac{\big(5\big)^2}{\big(QR\big)^2}\end{gathered}
:⟹
121
100
=
(QR)
2
(5)
2
\begin{gathered}\\ :\implies\:\sf \dfrac{100}{121} = \dfrac{25}{{QR}^{2}}\end{gathered}
:⟹
121
100
=
QR
2
25
\:
By cross multiplying :
\begin{gathered}\\ :\implies\:\sf 100\:\times\:{QR}^{2} = 25\:\times\:121\end{gathered}
:⟹100×QR
2
=25×121
\begin{gathered}\\ :\implies\:\sf {QR}^{2} \:\times\: 100 = 3025\end{gathered}
:⟹QR
2
×100=3025
\begin{gathered}\\ :\implies\:\sf {QR}^{2} = \dfrac{3025}{100} \end{gathered}
:⟹QR
2
=
100
3025
\begin{gathered}\\ :\implies\:\sf QR = \sqrt{\dfrac{3025}{100}} \end{gathered}
:⟹QR=
100
3025
\begin{gathered}\\ :\implies\:\sf QR = {\cancel{\dfrac{55}{10}}} \end{gathered}
:⟹QR=
10
55
\begin{gathered}\\ :\implies\:\underline{\boxed{\bf{\purple{QR = 5.5}}}}\:\bigstar\end{gathered}
:⟹
QR=5.5
★
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Therefore, length of side QR of ∆PQR is 5.5 cm.
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-3 and -2 is the pair of positive number whose sum is -5