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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 $w$ . Then, the length can be expressed as $w + 7$ . Since 4 rectangles form the 8-sided shape, the contributions to the perimeter must be considered.

Step 2

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

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Answer

The 8-sided shape consists of 4 rectangles. The perimeter can be calculated using the formula:

egin{align*} P &= 2( ext{lengths}) + 2( ext{widths})
&= 2(4(w + 7)) + 2(4w)
&= 8w + 56 + 8w
&= 16w + 56 = 70
ext{Now, solve for } w:
16w = 70 - 56
16w = 14
w = rac{14}{16} = 0.875
ext{Thus, the width } w = 3.5 ext{ cm and the length } l = 10.5 ext{ cm.}

dimensionally: w = 3.5 ext{ cm, } l = w + 7 = 10.5 ext{ cm.}

Step 3

Work out the area of the 8-sided shape.

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Answer

The area of one rectangle is given by $A = ext{width} imes ext{length} = 3.5 imes 10.5$ Therefore, the area of one rectangle is: $A = 3.5 imes 10.5 = 36.75 ext{ cm}^2$ Since there are 4 rectangles, the total area of the 8-sided shape is: $ext{Total Area} = 4 imes 36.75 = 147 ext{ cm}^2$

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