The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and witdh of this rectangle

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justaguide eNotes educator | Certified Educator

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We have that the area of a rectangular field is equal to 300 square meters and its perimeter is equal to 70 meters.

Let the length and the width of the field be L and W

Perimeter = 2(W + L) = 70

=> W + L = 35

=> W = 35 - L

Area = W * L = 300

=> (35 - L)* L = 300

=> 35 L  - L^2 = 300

=> L^2 - 35 L + 300 = 0

=> L^2 - 15 L - 20 L + 300 = 0

=> L( L-15) - 20( L- 15) = 0

=> (L - 20) ( L -15) = 0

So L can be 20 and 15

W = 15...

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hala718 eNotes educator | Certified Educator

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neela | Student

Area A = l*w, where l is length and w = width of the rectangle.

So l*w = 300 m^2 (given).

Perimeter P = 2(l+w) is the formula.

=> 2(l+w) = 70 m.

Therefore l+w = 70/2 = 35 m.

Therefore lw = 300 and l+w = 35.

So l and w are the roots of x^2-(l+w)x+lw = 0

x^2-35x+300 = 0.

(x-20)(x-15) = 0.

x-20 = 0, or x-15 = 0.

So x1 = l = 20 and x2 = w = 15.

So length and breadth of the rectangular field are 20 m and 15 respectively.

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