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The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3

Question 14

The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD. area of rectangle ABDE = area of triangle AFE + area of triangle BCD AB : AE = 1 : 3... show full transcript

Worked Solution & Example Answer:The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3

Step 1

Find an expression for the area of triangle AFE

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Answer

The area of triangle AFE can be calculated using the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

In triangle AFE, the base is AF = 24 cm, and the height AE can be calculated as:

$\text{Area of triangle AFE} = \frac{1}{2} \times 24 \times AE = 12AE$

Step 2

Link the area of the rectangle with the area of the triangles

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Answer

The area of rectangle ABDE is calculated as:

$\text{Area}_{ABDE} = AB \times AD = 24 \times 24 = 576 cm^{2}$

From the previous part, we have:

$\text{Area of triangle AFE} = 12AE$

Therefore, according to the problem statement:

$576 = 12AE + 12AE = 24AE$

Step 3

Solve for AE using the given ratio

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Answer

We arrange the equation for AE:

$AE = \frac{576}{24} = 24 cm$

Given the ratio of AB to AE is 1:3, we can verify:

If AB = 24 cm, then AE should be 3 times AB,

$AE = 3 \times 8 = 24 cm$

Thus, both calculations are consistent.

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