1.

The angle of a triangle are in the ratio 1:2:3 .Find the angle in radianssol: let the angle of triangle are A, B andCGiven:A:B:C=1:2:3Let=A=x, B=2x, C=3xA+B+C= 180°x+2x+3x=180°6x=180°x=30°put the value of x A=x A= 30°B=2xB=2×30= 60° ​

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Solution -

We Have ,

\begin{gathered} \large \sf{a_{5} +a_{7} = 52}\\ \\ \large \sf{ = a + 4d + a + 6d= 52}\\ \\ \large \sf2a + 10D \: \: - - - (1)\\ \\ \large \sf{a_{11} = a + 10d = 46} \\ \\ \end{gathered}

a

5

+a

7

=52

=a+4d+a+6d=52

2a+10d−−−(1)

a

11

=a+10d=46

♠ Multiplying Both Sides by 2 :

\begin{gathered}\large :\longmapsto\sf 2a + 20d = 92\: \: - - - (2) \\ \end{gathered}

:⟼2a+20d=92−−−(2)

♠ SUBTRACTING (1) From (2) , We get :-

\begin{gathered}\sf10d = 40 \\ \\ \sf d = \cancel{\frac{40}{10} }\\ \\ \PURPLE{ \Large :\longmapsto \UNDERLINE {\boxed{{\bf d = 4} }}}\end{gathered}

10d=40

d=

10

40

:⟼

d=4


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