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Sia ? 6 years, 6 months ago
Given : {tex}\triangle \mathrm{ABC}{\sim} \triangle \mathrm{PQR}{/tex} &
ar {tex}\triangle \mathrm{ABC}{/tex} = ar {tex}\Delta \mathrm{PQR}{/tex}
{tex}{/tex}To prove: {tex}\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}{/tex}
Since, {tex}\triangle \mathrm{ABC}{\sim} \Delta \mathrm{PQR}{/tex}
ar {tex}\triangle A B C=\text { ar } \triangle P Q R{/tex} (given)
{tex}\frac{{\Delta ABC}}{{ar\Delta PQR}} = 1{/tex}
{tex}\Rightarrow{/tex} {tex}\frac{{A{B^2}}}{{P{Q^2}}} = \frac{{B{C^2}}}{{Q{R^2}}} = \frac{{C{A^2}}}{{P{R^2}}} = 1{/tex}
[Using Theorem of area of similar Triangles]
{tex}\Rightarrow{/tex} AB = PQ, BC = QR & CA = PR
Thus, {tex}\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}{/tex}
Posted by Saurav Kumar 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
According to the question,
{tex}(x - 5)(x - 6) = \frac{{25}}{{{{\left( {24} \right)}^2}}}{/tex}
{tex}\Rightarrow x(x - 6) - 5(x - 6) = \frac{{25}}{{{{(24)}^2}}}{/tex}
{tex}\Rightarrow {x^2} - 6x - 5x + 30 - \frac{{25}}{{{{(24)}^2}}} = 0{/tex}
{tex}\Rightarrow {x^2} - 11x + 30 - \frac{{25}}{{{{(24)}^2}}} = 0{/tex}
{tex}\Rightarrow {x^2} - 11x + \frac{{30 \times {{24}^2} - 25}}{{{{(24)}^2}}} = 0{/tex}
{tex} \Rightarrow {x^2} - 11x + \frac{{30 \times 576 - 25}}{{{{(24)}^2}}} = 0{/tex}
{tex} \Rightarrow {x^2} - 11x + \frac{{17280 - 25}}{{{{(24)}^2}}} = 0{/tex}
{tex}\Rightarrow {x^2} - \frac{{264x}}{{24}} + \frac{{145}}{{24}} \times \frac{{119}}{{24}} = 0{/tex}
{tex}\Rightarrow {x^2} - \left( {\frac{{145}}{{24}} + \frac{{119}}{{24}}} \right)x + \frac{{145}}{{24}} \times \frac{{119}}{{24}} = 0{/tex}
{tex}\Rightarrow {x^2} - \frac{{145}}{{24}}x - \frac{{119}}{{24}}x + \frac{{145}}{{24}} \times \frac{{119}}{{24}} = 0{/tex}
{tex}\Rightarrow x\left( {x - \frac{{145}}{{24}}} \right) - \frac{{119}}{{24}}\left( {x - \frac{{145}}{{24}}} \right) = 0{/tex}
{tex}\Rightarrow \left( {x - \frac{{145}}{{24}}} \right)\left( {x - \frac{{119}}{{24}}} \right) = 0{/tex}
{tex}\Rightarrow x - \frac{{145}}{{24}} = 0{/tex} or {tex}x - \frac{{119}}{{24}} = 0{/tex}
{tex}\Rightarrow x = \frac{{145}}{{24}}{/tex} or {tex}x = \frac{{119}}{{24}}{/tex}
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Check NCERT solutions here : <a href="https://mycbseguide.com/ncert-solutions.html">https://mycbseguide.com/ncert-solutions.html</a>
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Guru Jatt 7 years, 1 month ago

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Supriya Tiwari 7 years, 1 month ago
0Thank You