Question

Mang jose plans to fence his rectangglular lot before he will plant mushrooms for his mushrooms production business.The perimeter of the lot is 40 meters and the area is 96 square meters.

Using the concept of the sum and product of roots of a quadratic equation,how would you determine the length and the width of the rectungular lot? Provide a quadratic equation representing this scenario

please i need the answer​

Answer 1

Given :-

• Perimeter of rectangular lot = 40m .
• Area = 96m².

Solution :-

Let us assume that, Length of rectangular lot is L m and Breadth is B m.

So,

→ 2(L + B) = 40

→ L + B = 20

→ L = (20 - B)

also,

→ L * B = 96

→ (20 - B) * B = 96

→ 20B - B² = 96

→ B² - 20B + 96 = 0

→ B² - 12B - 8B + 96 = 0

→ B(B - 12) - 8(B - 12) = 0

→ (B - 12)(B - 8) = 0

→ B = 12 or 8 .

Therefore,

• If Breadth 12 cm , Length = 8 cm.
• If Breadth 8 cm , Length = 12 cm.

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