The area of abcd
is 10cm^2 show that x^2 +6x =1

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Maths

GCSE

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The area of square ABCD is 10 cm^2 . Show that x^2 + 6x = 1 (requires diagram which I will draw on the whiteboard).

The area of a square is the length of one side squared (multiplied by itself), so for a square with side length 3, the area will be 32 or 3 x 3, which = 9. For a square with side length x, the area will be x2 .Given that the length of one side is 3 + x, the area will be (3+x)2 This can be written as (3+x) * (3+x), and to expand these brackets we will use the 'crab claw' method. We will take the first value in the first bracket, and times it by both values of the second bracket. So we will multiply 3 by 3 which is 9, and then 3 by x which is 3x. We will then take the second value in the first bracket and multiply is by both values in the second bracket. So we will multiply x by 3 which is 3x, and then x by x, which is x2. Now we will add together all the the values we have just found: x2 + 3x + 3x + 9. Because the only like terms are 3x and 3x, and 3x + 3x = 6x, the final equation we form after expanding the brackets will be x2 + 6x + 9.. Given that the area of the square is given as 10cm2, 10 must be equivalent to x2 + 6x + 9, so we form the equation x2 + 6x + 9 = 10. When balancing equations, you must do whatever you do on one side to the other side. Therefore if we take 9 away from the left hand side, we must take 9 away from the right hand side (10 - 9 = 1), leaving us with x2 + 6x = 1, and completing the question.

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