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kupik [55]
4 years ago
11

The length of a rectangle is 2 less than 3 times its width. If the area of the rectangle is 96cm², what is the length of the rec

tangle?
Mathematics
1 answer:
Crazy boy [7]4 years ago
7 0

Answer:

\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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