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a_sh-v [17]
2 years ago
9

The length of each side of a regular pentagon is increased by 8 inches, so the perimeter is now 65 inches. What is the original

length of each side of the regular pentagon
Mathematics
1 answer:
evablogger [386]2 years ago
8 0

<em>Here</em> as the <em>Pentagon</em> is <em>regular</em> so it's <em>all sides</em> will be of <em>equal length</em> . And if we assume It's each side be<em> </em><em><u>s</u></em> , then it's perimeter is going to be <em>(s+s+s+s+s) = </em><em><u>5s</u></em>.And as here , each <em>side</em> is increased by <em>8 inches</em> and then it's perimeter is <em>65 inches</em> , so we got that it's side after increament is<em> (s+8) inches</em> and original length is <em>s inches </em>. And if it's each side is <em>(s+8) inches</em> , so it's perimeter will be <em>5(s+8)</em> and as it's equal to <em>65 inches</em> . So , <em><u>5(s+8) = 65</u></em>

{:\implies \quad \sf 5(s+8)=65}

{:\implies \quad \sf 5s+5\times 8=65}

{:\implies \quad \sf 5s+40=65}

{:\implies \quad \sf 5s=65-40}

{:\implies \quad \sf 5s=25}

{:\implies \quad \sf s=\dfrac{25}{5}=5}

{:\implies \quad \bf \therefore \quad \underline{\underline{s=5\:\: Inches}}}

As we assumed the original side to be <em><u>s</u></em> .

<em>Hence, the original side's length 5 inches </em>

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