(i) The length of the longer side is 3 cm
(ii) The length of the longer side is 6 cm
(iii) The length of the longer side is 15 cm
Step-by-step explanation:
A rectangle has sides in the ratio 1 : 3, we need to find the length of the longer side if:
- The length of the shorter side is 1 cm
- The length of the shorter side is 2 cm
- The length of the shorter side is 5 cm
Let us use the ratio method to solve the problem
(i)
∵ The ratio of the two sides of the rectangle is 1 : 3
∵ The length of the shorter side is 1 cm
→ Shorter : Longer
→ 1 : 3
→ 1 : x
By using cross multiplication
∴ 1 × x = 1 × 3
∴ x = 3
∵ x represents the length of the longer side
∴ The length of the longer side = 3 cm
The length of the longer side is 3 cm
(ii)
∵ The ratio of the two sides of the rectangle is 1 : 3
∵ The length of the shorter side is 2 cm
→ Shorter : Longer
→ 1 : 3
→ 2 : x
By using cross multiplication
∴ 1 × x = 2 × 3
∴ x = 6
∵ x represents the length of the longer side
∴ The length of the longer side = 6 cm
The length of the longer side is 6 cm
(iii)
∵ The ratio of the two sides of the rectangle is 1 : 3
∵ The length of the shorter side is 5 cm
→ Shorter : Longer
→ 1 : 3
→ 5 : x
By using cross multiplication
∴ 1 × x = 5 × 3
∴ x = 15
∵ x represents the length of the longer side
∴ The length of the longer side = 15 cm
The length of the longer side is 15 cm
Learn more:
You can learn more about the ratio in brainly.com/question/4302397
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