Question

In the figure, length of the rectangle is (√2 + 1)metres and its breadth is (√2 − 1) metres (a) Find its area. (b) The area of a rectangle is 1 square metre and its length is (2 + √3)metres. Find its breadth correct to a centimetre. (√3 ≈ 1.732).​

Answer 1

Solution

1).

Given :-

• Lenght of rectangle = (√2 + 1) m
• Breadth of rectangle = (√2 - 1) m

Find :-

• Area of rectangle

Explanation

Required Formula

★ Area of rectangle = (Length × Breadth)

Keep required values,

==> Area of rectangle = (√2-1)(√2+1)

★ (a + b)(a-b) = (a² - b²)

==> Area of rectangle = [ (√2)² - (1)²]

==> Area of rectangle = 2 - 1

==> Area of rectangle = 1 m².

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2).

Given :-

• Area of rectangle = 1 m²
• Length of rectangle = (√3 + 2)

Find :-

• Breadth of rectangle = ?

Explanation

We Have,

★Area of rectangle = (Length × Breadth)

Let,

• Breadth be b.

Keep required values,

==> 1 = (√3+2)×b

==> b = 1/(√3+2)

Retionalize denominator

For this,

Multiply by (√3-2) Numerator & Denominator in R.H.S.

==> b = (√3 - 2)/(√3-2)(√3+2)

==> b = (√3-2)/(√3 ² - 4)

==> b = (√3 - 2)/(3 - 4)

==> b = (√3 - 2)/(-1)

==> b = (2 - √3)

( ★ √3 = 1.732 )

==> b = (2 - 1.732)

==> b = 0.268 m

Hence

• Breadth of rectangle = 0.268 m

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Note:-

★ 1m = 100cm

So , Breadth of rectangle will be in cm

==> 0.268 m = 26.8 cm

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