Question

he planned in such a way that it's base dimensions are (x+1) and (x+2). how much he has to dig? a) (x+1) (b) (x-2) (c) (x-3) (d) (x+2)​

Answer 1

SOLUTION

COMPLETE QUESTION

A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by

$\sf{v(x) = {x}^{3} + {x}^{2} - 4x - 4 }$

i) He planned in such a way that its base dimensions are (x + 1) and (x + 2). How much he has to dig

a) (x+1)

(b) (x-2)

(c) (x-3)

(d) (x+2)

EVALUATION

Here it is given that A builder wants to build a sump to store water in an apartment. The volume of the rectangular sump will be modelled by

$\sf{v(x) = {x}^{3} + {x}^{2} - 4x - 4 }$

We now simplify it as below

$\sf{v(x) = {x}^{3} + {x}^{2} - 4x - 4 }$

$\implies \: \sf{v(x) = {x}^{2} (x + 1) - 4(x + 1) }$

$\implies \: \sf{v(x) = ( {x}^{2} - 4) (x + 1) }$

$\implies \: \sf{v(x) = ( {x}^{2} - {2}^{2} ) (x + 1) }$

$\implies \: \sf{v(x) = ( x + 2 ) (x - 2)(x + 1) }$

Now the builder has planned in such a way that its base dimensions are (x + 1) & (x + 2)

Hence the builder has to dig

$\displaystyle \sf{ = \frac{v(x)}{(x + 1)(x + 2)} }$

$\displaystyle \sf{ = \frac{(x + 2)(x - 2)(x + 1)}{(x + 1)(x + 2)} }$

$\displaystyle \sf{ = x - 2}$

Hence the correct option is (b) (x-2)

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Answer 2

Answer:

b ( x-2) option is right