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Standard VIII

Mathematics

Concept of Ratio between 3 Quantities Using Line Segments

The sides of ...

Question

The sides of a triangle are in the ratio 3 : 4 : 5. The longest side is 12 cm longer than the shortest side.

Find the length of the shortest side.

20 cm

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18 cm

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9 cm

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15 cm

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Solution

The correct option is B
18 cm

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

Given that 5x = 3x + 12

$\Rightarrow$ 5x - 3x = 12

$\Rightarrow$ 2x = 12

$\Rightarrow$ x = 6

$∴$ Length of the shortest side = 3x = 3 $\times$ 6 = 18 cm

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The sides of a triangle are in the ratio 3 : 4 : 5. The longest side is 12 cm longer than the shortest side. Find the length of the shortest side.

The correct option is B 18 cm Let the sides be 3x, 4x and 5x. Given that 5x = 3x + 12 ⇒ 5x - 3x = 12 ⇒ 2x = 12 ⇒ x = 6 ∴ Length of the shortest side = 3x = 3×6 = 18 cm

The sides of a triangle are in the ratio 3 : 4 : 5. The longest side is 12 cm longer than the shortest side.

Find the length of the shortest side.

The correct option is B
18 cm

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

Given that 5x = 3x + 12

$\Rightarrow$ 5x - 3x = 12

$\Rightarrow$ 2x = 12

$\Rightarrow$ x = 6

$∴$ Length of the shortest side = 3x = 3 $\times$ 6 = 18 cm