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

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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option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

16 would be your answer