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maks197457 [2]
2 years ago
7

This is due like right now, please help me!!!!

Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
8 0

\bold{\huge{\orange{\underline{ Solution }}}}

\bold{\underline{ Given \: Rules}}

  • <u>The </u><u>sum</u><u> </u><u>of </u><u>the </u><u>number </u><u>in </u><u>each </u><u>of </u><u>the </u><u>four </u><u>rows </u><u>is </u><u>the </u><u>same </u>
  • <u>The </u><u>sum </u><u>of </u><u>the </u><u>numbers </u><u>in </u><u>each </u><u>of </u><u>the </u><u>three </u><u>columns </u><u>is </u><u>the </u><u>same</u>
  • <u>The </u><u>sum </u><u>of </u><u>any </u><u>row </u><u>does </u><u>not </u><u>equal </u><u>the </u><u>sum </u><u>of </u><u>any </u><u>column </u>

\bold{\underline{ Let's \: Begin}}

<u>According </u><u>to </u><u>the </u><u>Second</u><u> </u><u>rule </u><u>:</u><u>-</u>

\sf{ 75+b+83=76+80+d=a+81+85+78+c+e }

\sf{ 158 + b = 156 + d = 166 + a = 78 + c + e ...(1)}

<u>According </u><u>to </u><u>the </u><u>first </u><u>rule </u><u>:</u><u>-</u><u> </u>

\sf{ 75+76+a+78 = b+80+81+c = 83+86+d+e}

\sf{ 229 + a = 161 + b + c = 168 + d + e ...(2)}

<u>From </u><u>(</u><u> </u><u>1</u><u> </u><u>)</u><u> </u><u>we </u><u>got </u><u>:</u><u>-</u>

\sf{ 158 + b = 166 + a, 156 + d = 166 + a }

\sf{ b = 166 - 158 + a,  d = 166 - 156 + a }

\sf{ b = 8 + a,  d = 10 + a ...(3)}

<u>Subsitute </u><u>(</u><u>3</u><u>)</u><u> </u><u>in </u><u>(</u><u> </u><u>2</u><u> </u><u>)</u><u> </u><u>:</u><u>-</u>

\sf{229+a = 161+8+a+c = 168+10+a+e}

\sf{ 229+a = 169+a+c = 178+a+e}

<u>We</u><u> </u><u>can </u><u>write </u><u>it </u><u>as </u><u>:</u><u>-</u>

\sf{ 229+a = 169+a+c \:or\:229+a = 178+a+e}

\sf{ c = 299-169+a-a\:or\:e = 229-178+a-a}

\sf{ c = 60 \: and \: e = 51 }

<u>Subsitute </u><u>the </u><u>value </u><u>of </u><u>c </u><u>and </u><u>e </u><u>in </u><u>(</u><u> </u><u>1</u><u> </u><u>)</u><u>:</u><u>-</u>

\sf{ 158 + b = 156 + d = 166 + a = 78 + 60 + 51 }

\sf{ 158 + b = 156 + d = 166 + a = 189}

<u>Now</u><u>, </u>

\sf{ For \: b,  158 + b = 189 }

\sf{ b = 189 - 158 }

\sf{ b = 31}

\sf{ For \: d ,  156 + b = 189 }

\sf{ d = 189 - 156 }

\sf{ d = 33}

\sf{ For \: a,  166 + a = 189 }

\sf{ a = 189 - 166 }

\sf{ a = 23 }

Hence, The value of a, b, c, d and e is 23, 31 ,60 ,33 and 51 .

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Step-by-step explanation:

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ipn [44]
There are 2 way to solve this.

one using Pythagoras theorem and 2nd using trigonometry

so lets solve it by both

using Pythagoras theorem we know

base^2 + perpendicular^2 = hypotanes^2

6^2 + x^2 = 12^2

36 + x^2 = 144

x^2 = 144- 36 = 108

x = √(108) = √( 2×2×3×3×3)

= (2×3) √ (3) = 6 √3

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bow lets use trigonometry

we know
sin theta = perpendicular / hypotanes
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so
x = 12×√3 /2 = 6√3
7 0
3 years ago
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