Question

Area of football stadium is 3a2+14a +8
i. What can be the possible expression for the length of the stadium?
ii. What can be the possible expression for the breadth of the stadium?
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Answer 1

Given

Area =4a

2

+4a−3.

We know that

Area of rectangle = length × breadth

So, to find the possible expressions for the length and breadth we have to factorise the given expression.

Using the method of splitting the middle term,

4a+4a−3

=4a

2

+6a−2a−3

=2a(2a+3)−1(2a+3)

=(2a−1)(2a+3)

∴ length × breadth =(2a−1)(2a+3)

Hence, the possible expressions for the length and breadth of the rectangle are :

length =(2a−1) and breadth =(2a+3) or, length =(2a+3) and breadth =(2a−1).

Answer 2

Given:

The area of the football stadium is 3a2+14a +8

To Find:

i. What can be the possible expression for the length of the stadium?

ii. What can be the possible expression for the breadth of the stadium?

Solution:

We are given the area of the football stadium and we need to find the possible values of the length and the breadth of the football stadium, before that we need to factorize the given equation for which we will split the middle term so that we can factorize the equation, which goes as

$=3a^2+14a+8\\=3a^2+12a+2a+8\\=3a(a+4)+2(a+4)\\=(3a+2)(a+4)$

So,

(i) What can be the possible expression for the length of the stadium?

The possible expression can be (3a+2) or (a+4)

Hence, the possibility for the length is (3a+2) or (a+4).

(ii) What can be the possible expression for the breadth of the stadium?

the possible expression can be (3a+2) or (a+4)

Hence, the possible expression for the breadth is (3a+2) or (a+4).