Question

the area of a sqaure park is given by the expression [9x^2 - 24x +16] sq. m. Find its side​

Answer 1

Answer:

(3x ― 4) m

Step-by-step explanation:

As per the provided information in the given question, we have been provided with,

• Area of the square park = (9x² ― 24 + 16) m²

We've been asked to calculate the side of the square park.

Area of square is calculated by using the formula, Area of Square = Side × Side. Side times Side can be written as (Side)². Let us assume the side of the square park as S. Henceforth,

$\implies\sf {Area_{(SQ.)} = (Side)^2 } \;$

Substitute the values as per the given information and our assumption.

$\implies\sf {(9x^2 - 24x + 16) \; m^2 = (S)^2} \;$

Taking square roots on both sides. We get that,

$\implies\sf {\sqrt{ \Big \{ (9x^2 - 24x + 16) \; m^2\Big \}} = \sqrt{(S)^2}} \;$

This can be written as,

$\implies\sf {\sqrt{ \Big \{ (9x^2 - 24x + 16) \; m^2\Big \}} = S} \;$

It is known to us that a² — 2ab + b² gives (a ― b)². Here, the same pattern has been followed in the LHS inder square roots.

$\implies\sf {\sqrt{ \Big \{ (3x)^2 - 2(3x \times 4) + (4)^2 \; m^2\Big \}} = S} \;$

As, the expression is in the form of a² — 2ab + b² and we know that a² — 2ab + b² is equal to (a ― b)². Thus,

$\implies\sf {\sqrt{ (3x - 4)^2 \; m^2 } = S} \;$

Now, this can be written as,

$\implies\boxed{\sf { (3x - 4) \; m = S}} \;$

Therefore, the side of the square park is (3x ― 4) m.

$\rule{200}2$

Answer 2

Answer:

The length of the side is 8 meters.

Step-by-step explanation:

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