The length and breadth of a rectangle are 24 cm and 7 cm respectively. What must be the length of its diagonal (in cm)? A) 50 B)

Question

The length and breadth of a rectangle are 24 cm and 7 cm respectively. What must be the length of its diagonal (in cm)?

A) 50 B) 28 C) 25 D) 56​

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3 months 2021-11-06T14:27:49+00:00 2 Answers 0 views 0

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    0
    2021-11-06T14:29:11+00:00

    ⋆ DIAGRAM :

    \setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\tt\large{A}}\put(7.7,1){ \tt\large{B}}\put(9.5,0.7){\sf{\large{24 cm}}}\put(11.5,1){ \tt\large{C}}\put(8,1){\line(1,0){3.5}}\put(8,1){\line(0,2){2}}\put(11.5,1){\line(0,3){2}}\put(8,3){\line(3,0){3.5}}\put(11.6,2){\sf{\large{7 cm}}}\qbezier(8,1)(8,1)(11.5,3)\put(11.5,3){ \tt\large{D}}\put(11.3,1){\line(0,2){0.2}}\put(11.3,1.2){\line(2,0){0.2}}\end{picture}

    ⠀⠀⠀\rule{160}{1}

    ✩ Diagonal Biscects Rectangle in two Equal Right Angle Triangle.

    \underline{\textsf{By Pythagoras Theorem in $\Delta$ BCD :}}

    \dashrightarrow\sf\:\:(Diagonal)^2=(Length)^2+(Breadth)^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=(BC)^2+(CD)^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=(24\:cm)^2+(7\:cm)^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=576\:cm^2+49\:cm^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=625\:cm^2\\\\\\\dashrightarrow\sf\:\:BD=\sqrt{625\:cm^2}\\\\\\\dashrightarrow\sf\:\:BD=\sqrt{25\:cm \times 25\:cm}\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf BD=25\:cm}}\qquad\bigg\lgroup\bf Diagonal\bigg\rgroup

    \therefore\:\underline{\textsf{Hence, Length of Diagonal is C) \textbf{25 cm}}}.

    \rule{180}{2}

    ⠀⠀⠀⠀⠀⠀⠀⠀Shortcut Trick

    \begin{tabular}{|c |c | c|}\cline{1-3}l/b & b/l & h \\\cline{1-3}3 & 4 & 5 \\5 & 12 &13\\7 & 24&25 \\8 & 15&17\\\cline{1-3}\end{tabular}

    ✩ As we know Rectangle will be Biscected by Diagonal in two Equal Right Angle Triangle.

    ✩ It will must follow Pythagorean Triplet.

    ✩ From Above we can see it will follow 7, 24 and 25. So , Longest Side will be Diagonal i.e. 25 cm.

    \therefore\:\underline{\textsf{Hence, Length of Diagonal is C) \textbf{25 cm}}}.

    0
    2021-11-06T14:29:20+00:00

    ✩ Diagonal Biscects Rectangle in two Equal Right Angle Triangle.⠀☢ \underline{\textsf{By Pythagoras Theorem in $\Delta$ BCD :}} By Pythagoras Theorem in Δ BCD :	 \begin{gathered}\dashrightarrow\sf\:\:(Diagonal)^2=(Length)^2+(Breadth)^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=(BC)^2+(CD)^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=(24\:cm)^2+(7\:cm)^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=576\:cm^2+49\:cm^2\\\\\\\dashrightarrow\sf\:\:(BD)^2=625\:cm^2\\\\\\\dashrightarrow\sf\:\:BD=\sqrt{625\:cm^2}\\\\\\\dashrightarrow\sf\:\:BD=\sqrt{25\:cm \times 25\:cm}\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf BD=25\:cm}}\qquad\bigg\lgroup\bf Diagonal\bigg\rgroup\end{gathered} ⇢(Diagonal) 2 =(Length) 2 +(Breadth) 2 ⇢(BD) 2 =(BC) 2 +(CD) 2 ⇢(BD) 2 =(24cm) 2 +(7cm) 2 ⇢(BD) 2 =576cm 2 +49cm 2 ⇢(BD) 2 =625cm 2 ⇢BD= 625cm 2 	 ⇢BD= 25cm×25cm	 ⇢ BD=25cm	 	  ⎩⎪⎪⎪⎧	 Diagonal ⎭⎪⎪⎪⎫	 	 ⠀\therefore\:\underline{\textsf{Hence, Length of Diagonal is C) \textbf{25 cm}}}.∴ Hence, Length of Diagonal is C) 25 cm

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