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Nimfa-mama [501]
2 years ago
6

The length of a rectangle is 3 cm less than its width what are the dimensions of the rectangle if its area is 270 cm²

Mathematics
1 answer:
kupik [55]2 years ago
7 0

Given:

The length of a rectangle is 3 cm less than its width.

The area of the rectangle is 270 cm².

To find:

The dimensions of the rectangle.

Solution:

Let x be the width of the rectangle. Then,

\text{Length}=x-3

Area of a rectangle is:

\text{Area}=\text{Length}\times \text{width}

270=(x-3)(x)

270=x^2-3x

0=x^2-3x-270

Splitting the middle term, we get

x^2-18x+15x-270=0

x(x-18)+15(x-18)=0

(x-18)(x+15)=0

x=18,-15

Width of the rectangle cannot be negative. So, the only value of x is 18.

Width=18

Length=18-3

Length=15

Therefore, the length of the rectangle is 15 cm and the width of the rectangle is 18 cm.

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