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Here are two rectangles - Edexcel - GCSE Maths - Question 8 - 2019 - Paper 1

Question 8

Here are two rectangles. $QR = 10cm$ $BC = PQ$ The perimeter of $ABCD$ is $26cm$ The area of $PQRS$ is $45cm^2$ Find the length of $AB$.

Worked Solution & Example Answer:Here are two rectangles - Edexcel - GCSE Maths - Question 8 - 2019 - Paper 1

Step 1

For $PQ$ to find the length of $PQ$

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Answer

The area of rectangle $PQRS$ is given by the formula:

$ext{Area} = ext{length} imes ext{width}$
Let the length of $PQ$ be $x$ cm. Since $QR = 10$ cm, the area can be set up as:

$x imes 10 = 45$
Hence, we solve for $x$ :

$x = rac{45}{10} = 4.5 ext{ cm}$
Thus, the length of $PQ$ is $4.5$ cm.

Step 2

For the perimeter of $ABCD$ to find the length of $AB$

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Answer

The perimeter of rectangle $ABCD$ is defined as:

$ext{Perimeter} = 2 imes ( ext{length} + ext{width})$
Let the length of $AB$ be $y$ cm. The width $BC$ is equal to the length of $PQ$ , which is $4.5$ cm. Therefore, we can set up the equation as:

$2(y + 4.5) = 26$
Now, simplifying that:

$y + 4.5 = 13$
$y = 13 - 4.5$
$y = 8.5 ext{ cm}$
Thus, the length of $AB$ is $8.5$ cm.

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