Question

Ram has purchased the plot of land. He wants to construct a water tank on it. The area of the plot is (x^2 + 5x -14) m^2 , breadth is (x-2) m and depth of the water tank is x m.

Q1
If its length is 15 m what will be its area?
Q2
Give a possible value of x so that water is sufficient for a population of 720 for 10 days if on an average a person needs 100 litres of water per day...

Answer 1

If the length of the plot is 15 m then its area is 90 m²

The possible value of x is 8

Step-by-step explanation:

Given the area of the plot

$A(x)=x^2+5x-14$ m²

$\implies A(x)=x^2+7x-2x-14$

$\implies A(x)=x(x+7)-2(x+7)$

$\implies A(x)=(x+7)(x-2)$

Given breadth of the area = (x-2) m

Therefore, the length of the area

$=\frac{A(x)}{(x-2)}=\frac{(x+7)(x-2)}{(x-2)}$

$\implies \text{Length}=(x+7)$ m

Also given that the length is 15 m

Thus,

$x+7=15$

$\implies x=15-7=8$ m

Therefore, breadth of the plot

$=x-2=8-2=6$ m

Thus, the area of the plot

$A=15\times 6=90$ sq m

(ii) One person needs 100 litres of water per day

Therefore, 720 persons will need 72000 Litres = 72 cubic m of water per day

In 10 days, the water requirement = 720 cubic m

Thus, the volume of the tank should be 720 cubic m

Length x Breadth x Height = 720

$x(x+7)(x-2)=720$

Putting x = 8 in the above equation We get

$\text{LHS} = 8(8+7)(8-2)$

$\implies \text{LHS}=8\times 15\times 6=720=\text{RHS}$

Therefore, x=8 is the solution of the equation.

Hence, the value of x is 8.

Hope this answer is helpful.

Know More:

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