Question

A rectangle measures(2x-1)cm by(x+2)cm. Given that the area of the rectangle is 63cm². find the value of x​

Answer 1

Answer:

5cm

Step-by-step explanation:

A rectangle is a quadrilateral (4 sided polygon) with 2 opposite sides parallel and equal.

Area of a rectangle = length x breadth

Given that length = (2x - 1) , breadth = ( x + 2), Area = 63cm².

Since area = length x breadth

Area = (2x - 1) x ( x + 2)

(2x - 1)(x + 2) = 63

Expand the bracket

2x (x + 2) -1 ( x + 2) = 63

2x² + 4x - x - 2 = 63

2x² + 3x - 2 = 63

2x² + 3x -2 -63 = 0

2x² + 3x - 65 =0

We'll Solve the quadratic equation, we can solve using factorisation method.

Factor of -130 that is (- 65 x 2) that add up to +3 the coefficient of x

Factors = 13  and -10  

Rewrite equation

2x² - 10x + 13x - 65 = 0

Factorise

2x(x - 5) + 13 ( x - 5) = 0

2x + 13 = 0 or x - 5 = 0

2x = -13 or x = 5

Since we can't have a negative length then x = 5cm

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