Question

The reciprocal of 1+2⁻¹+3⁻¹+4⁰ is the side of a square in meters. The perimeter of the square is​

Answer 1

Solution :-

we know that,

• a^(-n) = 1/a^n .
• a^0 = 1
• Reciprocal of a = 1/a .

so,

→ 1 + 2^(-1) + 3^(-1) + 4^0

→ 1 + (1/2) + (1/3) + 1

→ 2 + {1/2 + 1/3}

→ 2 + {3 + 2/6}

→ 2 + (5/6)

→ (17/6)

then,

→ Side of square = reciprocal of (1+2⁻¹+3⁻¹+4⁰) = reciprocal of (17/6) = 1 / (17/6) = (6/17)

therefore,

→ Perimeter of square = 4 * side = 4 * (6/17) = (24/17) m (Ans.)

Hence, the perimeter of the square is (24/17) m or 1(7/17) m .

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Answer 2

Step-by-step explanation:

Given:1+2⁻¹+3⁻¹+4⁰

To find:The reciprocal of 1+2⁻¹+3⁻¹+4⁰ is the side of a square in meters. The perimeter of the square is?

Solution:

Step 1: Solve 1+2⁻¹+3⁻¹+4⁰

$= 1 + \frac{1}{2} + \frac{1}{3} + 1 \\ \\ = \frac{6 + 3 + 2 + 6}{6} \\ \\ = \frac{17}{6}$

Step 2: Write reciprocal of 17/6

Reciprocal of a is 1/a.

here,

Reciprocal is 6/17

Side of square = 6/17 meters

Step 3: Find perimeter of square

Perimeter = 4× side

$= 4 \times \frac{6}{17} \\ \\ = \frac{24}{17} \: m$

Final answer:

Perimeter of square is 24/17 meters or 1.41 meters.

Hope it helps you.

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