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3 years ago

What is the length of AC ? 3ft 4ft 9ft 18ft

Mathematics

1 answer:

WINSTONCH [101]3 years ago

5 0

ΔACB and ΔMNB are similar. Therefore the corresponding sides are in proportion:

$\dfrac{AC}{MN}=\dfrac{CB}{NB}\\\\MN=9\ ft\\CB=2\cdot3\ ft=6\ ft\\NB=3\ ft$

Substitute:

$\dfrac{AC}{9}=\dfrac{6}{3}\\\\\dfrac{AC}{9}=2\ \ \ \ |\cdot9\\\\AC=18\ ft$

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A rectangle has sides in the ratio 1:3 a)Write down the length of the longer side of the length of the shorter side is: (i) 1 cm

Lera25 [3.4K]

(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

#LearnwithBrainly

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