Question

If the base of a parallelogram is (x + 4), altitude to the base is (x – 3) and the area is (x^2 – 4), then what is the actual area equal to ?​

Answer 1

Answer:

Area of the parallelogram = base × altitude

= (x + 4) × (x – 3) = x^2 + 4x – 3x – 12

= x^2 + x – 12

Given, x^2 + x – 12 = x^2 – 4

=> x^2 + x – 12 = x^2 – 4

=> x = 8

Therefore actual area = 8^2 – 4 = 60 sq units.

Answer 2

Given:-

• Base of llgm = (x+4)
• Height of llgm = (x-3)
• Area of llgm = (x² - 4)

To Find:-

• Actual area of parallelogram.

Solution:-

$\sf \small\: \underline{\green{ area \: of \: parallelogram = base \times height}} \\ \sf\: (x {}^{2} - 4) = (x + 4) \times (x - 3) \\ \sf x {}^{2} - 4 = x {}^{2} - 3x + 4x - 12 \\ \sf \: x {}^{2} - 4 = x {}^{2} + 1x - 12 \\ \sf\: \cancel{ x {}^{2}} - 4 = \cancel{x {}^{2} } + 1x - 12 \\ \sf\: - 4 = x - 12 \\ \sf x = - 4 + 12 \\ \sf \: \boxed{ \bf{x = 8}}$

➸ Area of parallelogram,

= x² - 4

= (8)² - 4

= 64 -4

= 60 sq. units

Hence, the area of parallelogram is 60 sq. units.