Question

1. The sum of the two angle of an quadrilateral is 145 • The other two angle are in the radio 2:3. Find the angles.
2. The area of x-square field is 2025 square meter. Fund the cost of fencing the field at Rs. 15 per meter.​

Answer 1

${\underline{\underline{\bf{\blue{QueStion\;1\;:}}}}}$

The sum of the two angle of an quadrilateral is 145 • The other two angle are in the radio 2:3. Find the angles.

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${\underline{\underline{\bf{\green{AnswEr\;:}}}}}$

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GivEn:

• The sum of the two angle of an quadrilateral is 145°
• Ratio of other two angles = 2:3

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To find:

• Measure of angles?

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SoluTion:

${\underline{\bf{\bigstar\;As\;per\;givEn\;Question\;:}}}$

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The sum of the two angle of an quadrilateral is 145°

Ratio of other two angles = 2:3

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☯ Let these two angles be 2x and 3x.

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We know that,

Sum of all angles of a quadrilateral is 360°.

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$:\implies\sf 145^\circ + 2x + 3x = 360^\circ$

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$:\implies\sf 145^\circ + 5x = 360^\circ$

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$:\implies\sf 5x = 360^\circ - 145^\circ$

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$:\implies\sf 5x = 215^\circ$

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$:\implies\sf x = \cancel{ \dfrac{215^\circ}{5}}$

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$:\implies{\underline{\boxed{\bf{\pink{43^\circ}}}}}\;\bigstar$

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Therefore, Other measure of two angles are:

• 2x = 2 × 43 = 86°
• 3x = 3 × 43 = 129°

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${\underline{\underline{\bf{\blue{QueStion\;2\;:}}}}}$

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The area of a square field is 2025 m². Find the cost of fencing the field at Rs. 15 per meter.

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${\underline{\underline{\bf{\green{AnswEr\;:}}}}}$

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GivEn:

• The area of a square field is 2025 m².

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To find:

• Find the cost of fencing the field at Rs. 15 per meter.

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SoluTion:

☯ Let side of square field be x.

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${\underline{\bf{\bigstar\;As\;per\;givEn\;Question\;:}}}$

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The area of a square field is 2025 m².

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We know that,

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$\star\;\bf Area_{\;(square)} = side \times side$

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$\;\;\;\;\;\small\sf \underline{Putting\;values\;:}$

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$:\implies\sf x^2 = 2025$

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$\;\;\;\;\;\small\sf \underline{Taking\;sqrt.\;both\;sides\;:}$

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$:\implies\sf \sqrt{x^2} = \sqrt{2025}$

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$:\implies{\underline{\boxed{\bf{\pink{x = 45}}}}}\;\bigstar$

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$\therefore$ Side of square field is 45 m.

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We know that,

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$\star\;\bf Perimeter_{\;(square)} = 4 \times side$

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$\;\;\;\;\;\small\sf \underline{Putting\;values\;:}$

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$:\implies\sf Perimeter_{\;(field)} = 4 \times 45$

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$:\implies{\underline{\boxed{\bf{\pink{Perimeter_{\;(field)} = 180\;m}}}}}\;\bigstar$

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$\therefore$ The cost of fencing the field = 180 × 15 = Rs. 2700