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The area of square ABCD is 10 cm² - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

Question 4

The area of square ABCD is 10 cm². Show that $x^2 + 6x = 1$

Worked Solution & Example Answer:The area of square ABCD is 10 cm² - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

Step 1

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Answer

Given that the side length of the square is composed of two terms, the expression for the area can be written as:

$ext{Area} = ext{side}^2 = (3 + x)^2$

Setting this equal to the known area:

$(3 + x)^2 = 10$

Step 2

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Answer

Expanding the left-hand side:

$(3 + x)^2 = 3^2 + 2(3)(x) + x^2 = 9 + 6x + x^2$

Setting this equal to 10, we have:

$9 + 6x + x^2 = 10$

Subtract 10 from both sides:

$x^2 + 6x + 9 - 10 = 0$

This simplifies to:

$x^2 + 6x - 1 = 0$

Step 3

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101 rated

Answer

Rearranging the previous expression, we get:

$x^2 + 6x = 1$

Thus, the required result is shown.

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