Question

1. Find the length of the rectangle whose
(a) Area = 352 sq cm and breadth = 22 cm
(b)​

Answer 1

Given

• Area of the rectangle = 352 cm²
• Breadth of the rectangle = 22 cm

To find

• Length of the rectangle

Solution

Let the length of the rectangle be x cm.

Using formula,

Area of the rectangle = l × b

where,

• l = length of the rectangle
• b = breadth of the rectangle

Substituting the given values,

⟶ 352 = x × 22

⟶ 352/22 = x

⟶ 16 = x

The value of x = 16 cm

❖ Length of the rectangle = 16 cm

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Verification :

Substituting the value of length of the rectangle in 352 = x × 22

RHS

⟶ 16 × 22

⟶ 352

LHS = RHS

Hence, verified.

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Some related formulae :

• Perimeter of the rectangle = 2(l + b)
• Diagonal of rectangle = √l² + √b²
• Area of square = side × side
• Perimeter of square = 4 × side
• Diagonal of square = √2a
• Area of cube = side × side × side
• Area of cuboid = 2(lb + bh + hl)

Answer 2

$\huge\sf{\underline{To \: find}}:$

• Length of the rectangle.

$\large\bf{\underline{Given}}$

• Area of the rectangle = 352 cm²
• Breadth of the rectangle = 22 cm

Formula to be used

$\large\orange{\fbox\orange{\tt{Area\:of\:a\:rectangle\:=\:l×b}}}$

where,

l = length of the rectangle

b = breadth of the rectangle

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$\huge\bold{\underline{\underline{Solution}}}$

☞ let the length of this rectangle be 'x' cm.

Substituting the given values in the formula, we get –

$\sf{area = l \times b} \\ \implies\sf{352\:{cm}^{2} = 22\:cm\:{\tiny\times}\:x\:cm} \\ \implies \sf{x = \frac{{ \large \not}352}{{ \large\not}22} } \\ \implies \purple{\boxed{\bf{x = 16}}}$

∴ Length of this rectangle is 16cm.

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$\huge\green{\underline{\tt{Verification}}}✓$

Substituting the value of length found in - (352 = x × 22),

RHS =

→ 22 × 16

→ 352

RHS = LHS

Hence verified!

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✍️Relatable Formulae :-

• Area of rectangle = l×b
• Perimeter of rectangle = 2(l+b)
• Area of square = (side)²
• Perimeter of square = 4×side
• Area of cuboid = 2(lb + bh + hl)
• Area of a cube = (side)³

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