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Maths-

General

Easy

Question

Given the area of a square, factor it to find the side length.
Area = $36 x squared plus 120 x plus 100$

hint Hint:

Using the formula area = side2. find the side of the square by factoring the area .

The correct answer is: 6x + 10 is the side length of the square.

Ans:- 6x+10 is the side length of the square.
Given , A = $36 x squared plus 120 x plus 100$
Take out common factor 4 we get $4 open parentheses 9 x squared plus 30 x plus 25 close parentheses$
Write $9 x squared text as end text left parenthesis 3 x right parenthesis squared comma 30 x text as end text 2 left parenthesis 3 x right parenthesis left parenthesis 5 right parenthesis text and end text 25 text as end text 5 squared text we get end text straight A equals 4 open square brackets left parenthesis 3 x right parenthesis squared plus 2 left parenthesis 3 x right parenthesis left parenthesis 5 right parenthesis plus 5 squared close square brackets$
Applying $a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared text formula here end text a equals 3 x space semicolon space b equals 5$
We get $A equals 4 left parenthesis 3 x plus 5 right parenthesis squared$
But, area of square A = $left parenthesis text side end text right parenthesis squared$
$4 left parenthesis 3 x plus 5 right parenthesis squared equals left parenthesis text side end text right parenthesis squared not stretchy rightwards double arrow text side end text equals 2 left parenthesis 3 x plus 5 right parenthesis$
∴ length of side is 6x+10 .

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