Question

the length of a rectangular lot is 6 less than twice its width. If the area is 45 square cm. What is the length and the width of the rectangle​

Answer 1

The length and width of the rectangle​ are 9 cm and 5 cm if the length of a rectangular lot is 6 less than thrice its width and the area is 45 cm².

Correct question:

The length of a rectangular lot is 6 less than thrice its width. If the area is 45 square cm. What is the length and the width of the rectangle​?

Given:

Length of a rectangle = 6 less than thrice its width

Area of a rectangle = 45 cm²

To find: The length and the width of the rectangle​

Formula used:

Area of a rectangle = Length of rectangle × breadth of a rectangle

Solution:

Step 1: Make an equation according to the given data:

Let the width of a rectangle be b.

Length of a rectangle = 3b - 6 .......(1)

Step 2: Find the width of the rectangle​ :

Area of a rectangle = Length of rectangle ​× breadth of a rectangle

$\bf 45 = (3 b - 6 ) \times b \\\\45 = 3b^{2} - 6b \\\\3b^{2} - 6b = 45 \\\\3b^{2} - 6b - 45 = 0 \\\\3(b^{2} - 2b - 15) = 0$

[Taking 3 common]

$\bf b^{2} - 2b - 15 = 0 \\\\b^{2} - 5b + 3b - 15 = 0$

[Factorisation by middle-term splitting]

$\bf b(b - 5) + 3(b - 5) = 0 \\\\(b - 5) (b + 3) = 0 \\\\(b - 5) = 0 , (b + 3) = 0 \\\\b = 5 \ or \ b = - 3$

b = 5 cm

[Dimensions can't be negative]

Width of the rectangle​ = 5 cm

Step 3: Find the length of the rectangle​ :

Substitute b = 5 cm in eq.1

Length of a rectangle = $\bf 3b - 6$

Length of a rectangle = $\bf 3 \times 5 - 6$

Length of a rectangle = $\bf 15 - 6$

Length of a rectangle = 9 cm

Hence, the length and width of the rectangle​ are 9 cm and 5 cm.

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