Question

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Answer 1

Step-by-step explanation:

Step-by-step explanation:

1 + 3 = 41+3=4

This is expansion

Answer 2

Q2.

Given :

• Length of the rectangle is three times it's width.
• Perimeter of the rectangle is 96cm

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To find :

• The length and breadth of the rectangle

Concept :

In the question we are given the relation between length and width of a rectangle using which we will assume some variable for them. Then we are also given the perimeter of the rectangle and we do know that ,

$\dag\:\underline{\bf Perimeter~of~rectangle~=~2(l+b)}$

So using this formula and the value given we would frame an appropriate equation and then solving that we would get the final answer.

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Assumption :

• Let the width/breadth of the rectangle be b

According to the question ,

⠀⠀⠀⠀Length = 3 × width/breadth = 3 × b = 3b

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Solution :

According to the question ,

$\sf\: Perimeter~of~rectangle~=~96$

Now using the formula

$\sf\rightarrow\: 2(l+b)~=~96$

Substituting the assumed values

$\sf\rightarrow\: 2(3b+b)~=~96$

$\sf\rightarrow\: 2(4b)~=~96$

$\sf\rightarrow\: 8b~=~96$

$\sf\rightarrow\: b~=~\cancel{\frac{96}{8}}$

$\small{\underline{\boxed{\mathrm{\rightarrow\:b~=~12~cm}}}}$

Henceforth ,

⠀⠀⠀⠀⠀Length = 3 × b = 3 × 12 = $\small{\mathfrak\red{36~cm}}$

⠀⠀⠀⠀⠀Breadth/width = b = $\small{\mathfrak\red{12~cm}}$

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Q3.

Given :

• Present age of son is half the present age of his father.
• Ten years ago, father was thrice as old as his son.

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To find :

• The present age of father and son.

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Concept :

For this one also it remains the same we just need to form an appropriate equation and solve it.

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Assumption :

• Let the present age of father be x.

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Solution :

According to the question ,

Present age of son = Half the present age of father

⇒ Present age of son = $\sf\:\frac{1}{2} \times x$

⇒ Present age of son = $\sf\:\frac{x}{2}$

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Now ten years ago ,

Ages would be = Present age - 10

⠀⠀⠀⠀⠀Father's age = (x - 10)

⠀⠀⠀⠀⠀Son's age = $\sf\:\frac{x}{2}-10$

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Framing equation ,

$\sf\: Father's~age=3 \times Son's~age$

$\sf\to\:(x-10)=3 (\frac{x}{2}-10)$

$\sf\to\:(x-10)=3 (\frac{x-20}{2})$

$\sf\to\:(x-10)=\frac{3x-60}{2}$

$\sf\to\:2(x-10)=3x-60$

$\sf\to\:2x-20=3x-60$

$\sf\to\:2x-3x=20-60$

$\sf\to\:\cancel{-}x=\cancel{-}40$

$\small{\underline{\boxed{\mathrm{\to\:x~=~40~yrs}}}}$

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Henceforth ,

⠀⠀⠀⠀⠀Father's present age = $\small{\mathfrak\red{40~yrs}}$

Son's present age

⠀⠀⠀⠀⠀1/2 × x = 1/2 × 40 = $\small{\mathfrak\red{20~yrs}}$

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⠀⠀⠀⠀⠀⠀⠀⠀Hope it helps :D~

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