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The sides of this triangle are given in centimetres - OCR - GCSE Maths - Question 9 - 2023 - Paper 4

Question 9

The sides of this triangle are given in centimetres. The perimeter of the triangle is 80 cm. Find the length of each side of the triangle. You must show your workin... show full transcript

Worked Solution & Example Answer:The sides of this triangle are given in centimetres - OCR - GCSE Maths - Question 9 - 2023 - Paper 4

Step 1

Find the expression for the perimeter

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Answer

To find the perimeter of the triangle, we will sum up the lengths of the three sides:

Side 1: $x + 5$
Side 2: $2x + 8$
Side 3: $3x + 1$

The total perimeter is given as 80 cm, hence the equation is:

(x + 5) + (2x + 8) + (3x + 1) = 80

Step 2

Simplify and solve for x

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Answer

Now, let's simplify the equation:

6x + 14 = 80

Subtract 14 from both sides:

6x = 66

Now, divide by 6 to solve for x:

x = 11

Step 3

Calculate the lengths of each side

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Answer

Now that we have found $x$ , we can find the length of each side:

Side 1:

x + 5 = 11 + 5 = 16 ext{ cm}$$ - Side 2:

2x + 8 = 2(11) + 8 = 22 + 8 = 30 ext{ cm}$$

Side 3:

3x + 1 = 3(11) + 1 = 33 + 1 = 34 ext{ cm}$$

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