khushi asked in Science & MathematicsMathematics · 2 months ago

# A rectangle’s length is 3 cm more than its width. Find the dimensions of the rectangle if its area is 20 cm2.?

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• 2 months ago

x * (x + 3) = 20

x^2 + 3x = 20

x^2 + 3x + 1.5^2 = 20 + 1.5^2

(x + 1.5)^2 = 20 + 2.25

(x + 1.5)^2 = 22.25

(1/4) * (2x + 3)^2 = (1/4) * 89

(2x + 3)^2 = 89

2x + 3 = +/- sqrt(89)

2x = -3 +/- sqrt(89)

x > 0

2x = (sqrt(89) - 3)

x = (sqrt(89) - 3) / 2

• David
Lv 7
2 months ago

Let its length be x+3 and its width be x

Area of rectangle (x+3)*x = 20 or x^2 +3x -20 = 0

Solving the quadratic equation x = +3.216990566

Therefore: length = 6.216990566 cm and width = 3.21699056 cm

Check: 6.216990566*3.216990566 = 20 square cm

• 2 months ago

x(x + ) = 20

x^2 + 3x  = 20

Complete the Square

(x + 3/2)^2 - ( 3/2)^2 = 20

(x+ 3/2)^2 - 9/4 = 20

(x + 3/2)^2 = 20  + 9/4 = 89/4

Square root both sides

x + 3/2 = +/-sqrt(89) / 2

x = - 3/2 +/- sqrt(89) / 2

x = - 3/2 +/- 9.4339.... / 2

x = 6.4339... / 2

x = 3.2169...

& x + 3 = 6.2139....