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Here is a rectangle - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 3

Question 6

Here is a rectangle. The length of the rectangle is 7cm longer than the width of the rectangle. 4 of these rectangles are used to make this 8-sided shape. The per... show full transcript

Worked Solution & Example Answer:Here is a rectangle - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 3

Step 1

The length of the rectangle is 7cm longer than the width of the rectangle.

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Answer

Let the width of the rectangle be denoted as $w$ cm. Then, the length can be expressed as $w + 7$ cm.

Step 2

The perimeter of the 8-sided shape is 70cm.

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Answer

The 8-sided shape is formed by combining 4 rectangles. Since each rectangle has two widths and two lengths, the perimeter can be expressed as:

$P = 2(w + 7) + 2w + 2(w + 7) + 2w = 70$

This simplifies to:

$P = 2(4w + 14) = 70$

From here, we simplify to find the value of $w$ :

$4w + 14 = 35 \\ 4w = 21 \\ w = 5.25 ext{ cm}$

Step 3

Work out the area of the 8-sided shape.

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Answer

Now that we have the width, we can find the length:

$l = w + 7 = 5.25 + 7 = 12.25 ext{ cm}$

The area of one rectangle is:

$A = l imes w = 12.25 imes 5.25 \\ A = 64.3125 ext{ cm}^2$

Since there are 4 rectangles, the total area of the 8-sided shape is:

$ext{Total Area} = 4A = 4 imes 64.3125 = 257.25 ext{ cm}^2$

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