Question

A model of a boat is made on a scale of 1:4. The model is 120cm long. The
full size of the boat has a width of 60cm. What is the width of the scale
model?

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ A model of a boat is made on a scale of 1:4

✭ The model is 120 cm long & the real boat is 60 cm in breadth

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Width of the scale model?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here as per the Question,

›› $\displaystyle\sf Scale \ Factor = 1:4$

›› $\displaystyle\sf k = \dfrac{1}{4}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

➝ $\displaystyle\sf Length_{model} = k \times length_{ship}$

➝ $\displaystyle\sf 120 = \dfrac{1}{4} \times length_{ship}$

➝ $\displaystyle\sf 120\times 4 = length_{ship}$

➝ $\displaystyle\sf \purple{length_{ship} = 480 \ cm}$

Area of the ship will be,

»» $\displaystyle\sf Area_{ship} = Length\times Breadth$

»» $\displaystyle\sf Area_{ship} = 480\times 60$

»» $\displaystyle\sf \orange{Area_{ship} = 28800 \ cm^2}$

We know that,

➳ $\displaystyle\sf Area_{model} = k^2\times Area_{ship}$

➳ $\displaystyle\sf Length\times Width = k^2\times Area_{ship}$

➳ $\displaystyle\sf 120\times Width = (\dfrac{1}{4})^2\times 28800$

➳ $\displaystyle\sf 120\times Width = \dfrac{1}{16}\times 28800$

➳ $\displaystyle\sf 120\times Width = 1800$

➳ $\displaystyle\sf Width = \dfrac{1800}{120}$

➳ $\displaystyle\sf \pink{Width = 15 \ cm}$

$\displaystyle\sf \therefore\:\underline{\sf Width \ of \ the \ model \ is \ 15cm}$

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