Question

Q. The area of the rectangular lot is x² – 13x + 30 in square meters. If it's width is x – 3 meters, what is it's length?
a. x – 10 meters
b. x – 6 meters
c. x – 12 meters
d. x – 5 meters

Answer 1

Answer:

Answer is a. x - 10 meters

Step-by-step explanation:

x square - 13 x + 30

= x square - 10x + 3x + 30

= x (x - 10) - 3(x - 10)

= ( x- 3 ) ( x- 10 ) = x square - 13x + 30

Answer 2

GIVEN :-

The Area (a) of the Rectangular Plot = $\bold {x^2 - 13x + 30}\:m^2$

Width [Breadth] (b) of the Rectangular Plot = x - 3 m

TO FIND :-

The Length (l) of the Rectangular Plot

FORMULA USED :-

$Area\:of\:a\:Rectangle = Length * Breadth\:[Width]$

SOLUTION :-

Let the Length of the Rectangle be x m

Substituting the Given Values in the Formula given above, we get the Equation -

$x^2 - 13x + 30 = (x) * (x - 3)$

Now,

Factorize the Area to its Simplest Form : So, we get the Equation as -

$(x - 10)(x - 3) = (x - 3) * (x)$

Solving out the Factorized Equation, we get the Length (l) of the Rectangle as -

$(x - 10)(x - 3) = (x - 3) * (x)\\\\As\:(x - 3)\:is\:common\:in\:both\:LHS\:and\:RHS, strike\:out\:them :-\\\\So,\:Therefore,\:(x - 10) = x$

CONCLUSION :-

The Length (l) of the Rectangular Plot is (x - 10) m

∴ Option A is the Right Answer...