Question

Area of two similar triangles, ∆ABC and ∆PQR are 100 cm² and 121 cm² respectively. If BC=5cm, then QR is-​

Answer 1

Answer:

Measure of QR is 5.5 cm.

Step-by-step explanation:

We're given with, ∆ABC∼∆PQR.

Area of ∆ ABC = 100 cm²

Area of ∆ PQR = 121 cm²

Side BC of ∆ABC = 5 cm.

When two triangles are similar the ratio of the area of triangles is proportional to the square of the ratio of their corresponding sides.

$\longrightarrow{\rm{\dfrac{ar(ABC)}{ar(PQR)} = \dfrac{(BC)^{2} }{(QR)^{2}}}}$

$\longrightarrow{\rm{\dfrac{100}{121} = \dfrac{(5)^{2} }{(QR)^{2}}}}$

$\longrightarrow{\rm{\dfrac{100}{121} = \dfrac{25}{(QR)^{2}}}}$

$\longrightarrow{\rm{100 \times {QR}^{2} = 121 \times 25}}$

$\longrightarrow{\rm{100 \times {QR}^{2} = 3025}}$

$\longrightarrow{\rm{100 \times {QR}^{2} = 3025}}$

$\longrightarrow{\rm{ {QR}^{2} =30.25}}$

$\longrightarrow{\rm{ {QR} = \sqrt{30.25}}}$

$\longrightarrow{\rm{ {QR} = 5.5}}$

Therefore, measure of QR is 5.5 cm.

Answer 2

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,

$\\ :\implies\:\sf \Bigg\{\dfrac{ar\big(\triangle{ABC}\big)}{ar\big(\triangle{PQR}\big)}\Bigg\} = {\Bigg\{\dfrac{BC}{QR}\Bigg\}}^{2}$

$\\ :\implies\:\sf \dfrac{100}{121} = \dfrac{\big(5\big)^2}{\big(QR\big)^2}$

$\\ :\implies\:\sf \dfrac{100}{121} = \dfrac{25}{{QR}^{2}}$

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By cross multiplying :

$\\ :\implies\:\sf 100\:\times\:{QR}^{2} = 25\:\times\:121$

$\\ :\implies\:\sf {QR}^{2} \:\times\: 100 = 3025$

$\\ :\implies\:\sf {QR}^{2} = \dfrac{3025}{100}$

$\\ :\implies\:\sf QR = \sqrt{\dfrac{3025}{100}}$

$\\ :\implies\:\sf QR = {\cancel{\dfrac{55}{10}}}$

$\\ :\implies\:\underline{\boxed{\bf{\purple{QR = 5.5}}}}\:\bigstar$

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• Therefore, length of side QR of ∆PQR is 5.5 cm.

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