Question

the area of 2 rectangular field are given. find the dimensions :-
1. x^2+5x-24
2. 3x^2-5x-12

Answer 1

Hi there !!

In this question, we're required to find the area of rectangular fields.
This can be done by factorising them

1. x² + 5x - 24

Here's , the splitting of middle term is possible.
So, a × b = -24 and a + b = 5

So,

${x}^{2} + 8x - 3x - 24$
By taking out the common factor,
it can be written as,

$x(x + 8) - 3(x + 8)$
Taking common factor as x + 8,
we have,

$(x - 3)(x + 8)$
So,

One of The possible dimensions can be
Length = x - 3
Breadth = x + 8

OR

Length = x + 8
Breadth = x - 3

2. 3x² - 5x - 12
Using the method of splitting of middle term,
we know that ,
ab = -12 × 3 = -36
a + b = -5
-) a = 9
b = -4

So,

3x² + 9x - 4x - 12
Taking out common factor,
we have,

$= 3x(x + 3) - 4(x + 3)$

taking x + 3 as common factor,
we have,

$= (3x - 4)(x + 3)$

One of the possible dimensions can be
Length = 3x - 4
Breadth = x + 3

OR

Length = x + 3
Breadth = 3x - 4

Answer 2

The dimensions can be found by factorising the given eq.

1. x^2 + 5x - 24
= (x-3)(x+8)
therefore, the dimensions are x-3 and x+8..where x>3

2. 3x^2 -5x -12
= (3x+4)(x-3)
therefore, the dimensions are x-3 and 3x+4....where x>3

x is greater than 3 because if it is 3 or smaller then the result can't be the dimension of a park.

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