$Ritika has a square flower garden of area 49 a^{2} - 81$ sq. m. On representing the above area in the simplest form, it will be equal to sq. m.

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Solution

The correct option is B 14
Given

$Area of the square flower garden = 49 a^{2} - 81 s q . m .$

We observe:
$49 a^{2} = 7 \times 7 \times a \times a = (7 a)^{2}$

$81^{2} = 9 \times 9 = (9)^{2}$

So, the area of the square garden can be expressed as:

$49 a^{2} - 81 = (7 a)^{2} - (9)^{2}$

$We know, x^{2} - y^{2} = (x + y) (x - y)$

$So, x = 7 a a n d y = 9$

$So, 49 a^{2} - 81 = (7 a + 9) (7 a - 9)$

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Ritika has a square flower garden of area 49a2−81 sq. m. On representing the above area in the simplest form, it will be equal to sq. m.

The correct option is B 14Given Area of the square flower garden=49a2−81 sq. m. We observe: 49a2=7×7×a×a=(7a)2 812=9×9=(9)2 So, the area of the square garden can be expressed as: 49a2−81=(7a)2−(9)2 We know, x2−y2=(x+y)(x−y) So, x=7a and y=9 So, 49a2−81=(7a+9)(7a−9)

$Ritika has a square flower garden of area 49 a^{2} - 81$ sq. m. On representing the above area in the simplest form, it will be equal to sq. m.