Question

In️ abc find the value of the hypotenuse ac.ab= 5 cm, bc = 12 cm​

Answer 1

$\huge{\underline{\underline{\blue{\tt{\bold{Given\::}}}}}}$

• $\sf{ab\:=\:5\:cm}$

${\bold{\footnotesize{\blacksquare{\:Base}}}}$

• $\sf{bc\:=\:12\:cm}$

${\bold{\footnotesize{\blacksquare{\:Perpendicular}}}}$

${ }$

$\huge{\underline{\underline{\blue{\tt{\bold{Find\::}}}}}}$

• $\sf{ac\:=\:?}$

${\bold{\footnotesize{\blacksquare{\:Hypotenuse}}}}$

$\huge{\underline{\underline{\blue{\tt{\bold{Solution\::}}}}}}$

• $\bf{(H)}^{2}\:=\:{(P)}^{2}\:+\:{(B)}^{2}$

$\sf{\pink{We,\:know\:that\:-}}$

$\:\:\:\:\:\:\:\Rsh{\sf{\bold{(ac)}^{2}}\:=\:{\bold{(ab)}}^{2}\:+\:{\bold{(bc)}^{2}}}$

$\:\:\:\:\:\:\:\Rsh{\sf{(ac)}^{2}\:=\:{(12)}^{2}\:+\:{(5)}^{2}}$

$\:\:\:\:\:\:\:\Rsh{\sf{(ac)}^{2}\:=\:144\:+\:25}$

$\:\:\:\:\:\:\:\Rsh{\sf{(ac)}^{2}\:=\:169}$

$\:\:\:\:\:\:\:\Rsh{\sf{(ac)\:=\:{\sqrt{169}}}}$

$\:\:\:\:\:\:\:\Rsh{\sf{(ac)\:=\:13}}$

${ }$

$\:\:\:\:\:\:\:\:\:\:\therefore{\underline{\sf{Hence,\:the\:hypotenuse\:is}\:{\bold{13\:cm}}}}$

Answer 2

Step-by-step explanation:

$\huge{\red{\mathfrak{\sf{Question\:2}}}}$

${ }$

$\Large{\bf{\blue{Given\::}}}$

$\footnotesize{\sf{By\:adding\:8\:in\:one\:number\:and\:divide\:its}}$$\footnotesize{\sf{result\:with\:2\:we\:get\:the\:answer\:10}}$

${ }$

$\Large{\bf{\blue{Find\::}}}$

$\footnotesize{\sf{Show\:this\:in\:equation\:form}}$

${ }$

$\Large{\bf{\blue{Solution\::}}}$

$\footnotesize{\sf{Let\:say\:number\:is\:x}}$

$\sf{By\:adding\:8\:in\:one\:number\:\rightarrow\:x\:+\:8}$

$\sf{Divide\:its\:result\:with\:2\:\rightarrow\:(x\:+\:8)\:/\:2}$

$\sf{We\:get\:10}$

$\sf{Equation\:\rightarrow\:(x\:+\:8)\:/\:2\:=\:10}$

$\:\Box\:{\bold{\pink{\bf{(x\:+\:8)\:/\:2\:=\:10}}}}\:\sf{is\:the\:required\:equation}$

${ }$

$\bf{Solving}$

$\:\:\:\:\:\:\:\:\:\Longrightarrow\sf{x\:+\:8\:=\:20}$

$\:\:\:\:\:\:\:\:\:\Longrightarrow\sf{x\:=\:12}$

$\:\:\:\:\:\:{\bold{\purple{†}}}{\sf{\underline{\bold{(x\:+\:8)\:/\:2\:=\:10\:and\:number\:is\:12}}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:{\bold{━━━━━━━━━━━━━━━}}$

$\huge{\red{\mathfrak{\sf{Question\:3}}}}$

${ }$

$\Large{\bf{\blue{Given\::}}}$

$\footnotesize{\sf{2x \:+ \:3\: =\: 5}}$

${ }$

$\Large{\bf{\blue{Find\::}}}$

$\footnotesize{\sf{Write\: this\: in \:statement\: form}}$

${ }$

$\Large{\bf{\blue{Solution\::}}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{2x\:+\:3\:=\:5}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{2x\:=\:5\:-\:3}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{2x\:=\:2}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow\sf{x\:=\:}{\bold{1}}$

$\:\:\:\:\:\:\:\:\:\:{\bold{\purple{†}}}{\sf{\underline{\:When\:you\:add\:3\:from\:2x\:,\:you\:left\:with\:5}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:{\bold{━━━━━━━━━━━━━━━}}$

$\huge{\red{\mathfrak{\sf{Question\:4}}}}$

${ }$

$\Large{\bf{\blue{Given\::}}}$

$\footnotesize{\sf{x\: +\: 6 \:=\: 15}}$

${ }$

$\Large{\bf{\blue{Find\::}}}$

$\footnotesize{\sf{Value\:of\:x}}$

${ }$

$\Large{\bf{\blue{Solution\::}}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{x\:+\:6\:=\:15}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{x\:=\:15\:-\:6}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{x\:=\:9}}$

$\:\:\:\:\:\:\:\:\:\:{\bold{\purple{†}}}{\sf{\underline{\:So,\:the\:value\:of\:x\:is\:9}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:{\bold{━━━━━━━━━━━━━━━}}$

$\huge{\red{\mathfrak{\sf{Question\:5}}}}$

${ }$

$\Large{\bf{\blue{Given\::}}}$

$\footnotesize{\sf{Ravi\:and\:Arjun\:=\:3\::\:7}}$

$\footnotesize{\sf{Its\:addition\:=\:100}}$

$\Large{\bf{\blue{Find\::}}}$

$\footnotesize{\sf{Numbers\:of\:marbles\:of\:both}}$

$\Large{\bf{\blue{Solution\::}}}$

$\small\sf{Let\:Ravi\:and\:Arjun\:have\:3x\:and\:7x\:marbles\:respectively}$

$\bf{\underline{According\:to\:the\:question}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{3x\:+\:7x\:=\:100}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{10x\:=\:100}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{x\:100\:\div\:10}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\sf{x\:=\:10}}$

$\sf{\bold{Hence,}}$

$\therefore{\sf{Ravi\:have\:=\:3x\:=\:3\:\times\:10}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\bf{\:30\:marbles}}$

$\therefore{\sf{Arjun\:have\:=\:7x\:=\:7\:\times\:10}}$

$\:\:\:\:\:\:\:\:\::\:\Longrightarrow{\bf{\:70\:marbles}}$

${ }$

$\:\:\:\:\:\:\:\:\:\:{\bold{\purple{†}}}{\sf{\underline{\bold{\:So,\:Ravi\:have\:30\:marbles}}}}$

$\:\:\:\:\:\:\:\:\:\:{\bold{\purple{†}}}{\sf{\underline{\bold{\:And\:Arjun\:have\:70\:marbles}}}}$