The sides of a triangle are in the ratio 3 : 4 : 5. The longest side is 12 cm more than the shortest side. Find the length of the shortest side. [2 Marks]

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Solution

Let the measure of sides be 3x, 4x and 5x.

Given that 5x = 3x + 12 cm

$\Rightarrow$ 2x = 12 cm

$\Rightarrow$ x = 6 cm [1 Mark]

$∴$ Length of the shortest side = 3x = 3 $\times$ 6 = 18 cm [1 Mark]

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The sides of a triangle are in the ratio 3 : 4 : 5. The longest side is 12 cm more than the shortest side. Find the length of the shortest side. [2 Marks]

Let the measure of sides be 3x, 4x and 5x. Given that 5x = 3x + 12 cm ⇒ 2x = 12 cm ⇒ x = 6 cm [1 Mark] ∴ Length of the shortest side = 3x = 3×6 = 18 cm [1 Mark]

Let the measure of sides be 3x, 4x and 5x.

Given that 5x = 3x + 12 cm

$\Rightarrow$ 2x = 12 cm

$\Rightarrow$ x = 6 cm [1 Mark]

$∴$ Length of the shortest side = 3x = 3 $\times$ 6 = 18 cm [1 Mark]