A square is cut from a piece of cardboard in the shape of a right triangle, with two perpendicular sides 16 cm and 24 cm. Find the side of the largest possible square the can be cut.

Correct Option - 4


Detailed Solution:

Let x cm be the side of the square, in the figure.

 

ABC and BFE are similar triangles, AC = 24? x cm

EF = 16? x cm $\Rightarrow \frac{BC}{AC}=\frac{EF}{BE}$

$\Rightarrow \frac{x}{(12-x)}=\frac{(8-x)}{x}$ $\frac{}{}\frac{}{}$

x2 = (16? x) (24? x) = x = 9.6 cm

<div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"></picture></div><div class="figure"><div><div><picture><source srcset="" media=" (max-width: 500px)"></picture></div><div>Let x cm be the side of the square, in the figure.</div><div>&nbsp;</div><div><picture><img src="https://images.shiksha.com/mediadata/images/1754905007phpjoNh0P.jpeg" alt="" width="184" height="131" loading="lazy"></picture></div></div><p>ABC and BFE are similar triangles, AC = 24? x cm</p><p>EF = 16? x cm <span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mfrac> <mrow> <mi>B</mi> <mi>C</mi> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>E</mi> <mi>F</mi> </mrow> <mrow> <mi>B</mi> <mi>E</mi> </mrow> </mfrac> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mo stretchy="false"> (</mo> <mn>1</mn> <mn>2</mn> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo stretchy="false"> (</mo> <mn>8</mn> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>x</mi> </mrow> </mfrac> </mrow> </math> </span><math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math></p><p>x2 = (16? x) (24? x) = x = 9.6 cm</p></div></div>

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