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RandomLollipop

19.06.2021

Mathematics

$\boxed{\sf Length \ of \ the \ rectangle = 16 \ cm}$

Given:

Area of the rectangle = 96 cm²

Length of the rectangle = 2 less than 3 times it's width

To Find:

Length of the rectangle

Step-by-step explanation:

Let the width of the rectangle be 'w'.

So,

Length of the rectangle = 3w - 2

$\sf \implies Area \ of \ rectangle = Length \times Width \\ \\ \sf \implies 96 = (3w - 2) \times w \\ \\ \sf \implies 96 = 3 {w}^{2} - 2w \\ \\ \sf \implies 3 {w}^{2} - 2w = 96 \\ \\ \sf \implies 3 {w}^{2} - 2w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - (18 - 16)w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - 18w + 16w - 96 = 0 \\ \\ \sf \implies 3w(w - 6) + 16(w - 6) = 0 \\ \\ \sf \implies (w - 6)(3w + 16) = 0 \\ \\ \sf \implies w - 6 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: 3w + 16 = 0 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: 3w = - 16 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: w = - \frac{16}{3}$

Width can't be negative. So,

Width of the rectangle = 6

Length of the rectangle = 3w - 2

= 3(6) - 2

= 18 - 2

= 16 cm

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