What is the maximum total area that 450cm of string can enclose if it is used to form the perimeters of two adjoining rectangles
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Answer:
Step-by-step explanation:
A quadratic polynomial is given to us and we need to find its factorised form . The given quadratic polynomial is ,
And this equation is similar to the equation in ax² + bx + c form . So in order to factorise it .
Step 1: <u>Multiply </u><u>the </u><u>coefficient </u><u>of </u><u>x²</u><u> </u><u>with </u><u>the </u><u>constant</u><u> </u><u>term </u><u>.</u>
Here the coefficient of x² is 12 and the constant term is 1 . So on multiplying them we get 12*1= 12 .
Step 2: <u>Look </u><u>out</u><u> </u><u>for </u><u>the </u><u>possible</u><u> </u><u>factors </u><u>of </u><u>the </u><u>number</u><u> </u><u>.</u>
Here the obtained number is 12 . So the possible factors of 12 is
- 1 *12
- -1*-12
- 2*6
- -2*-6
- 4*3
- -4*-3
Step3: <u>Choose </u><u>the </u><u>factor </u><u>whose </u><u>sum </u><u>is </u><u>equal </u><u>to </u><u>the </u><u>coefficient</u><u> </u><u>of </u><u>the </u><u>middle</u><u> </u><u>term </u><u>.</u>
Here we can see that the middle term is 7 . And the sum of 4 and 3 is equal to 7 . Hence here we will break 7x as 4x + 3x .
Step 4: <u>After </u><u>proper</u><u> </u><u>arrangements</u><u> </u><u>take </u><u>out</u><u> the</u><u> </u><u>common</u><u> </u><u>term </u><u>and </u><u>then </u><u>factorise</u><u>.</u>
After suitable rearrangment we get ,