Question

The area of a rectangle is found by multiplying its width by its length. The perimeter of a rectangle is found
by adding up all four of its sides. For instance, a plot of land that measures 20 metres by 10 metres has an
area of 20 x 10 - 200 square metres and a perimeter of 20+10+20+10 -2(20) 2(10) - 60 metres. The
neighbouring plot has double the area compared to this one. What is the length and width of the second
plot if its perimeter is 40 metres greater than the perimeter of the first one?

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Answer 1

Answer:

by adding length and breadth of rectangle and multypling it by 2

Answer 2

Correct answer:

40cm

Explanation:

For a rectangle, area is A=lw and perimeter is P=2l+2w, where l is the length and w is the width.

Let x = length and x−4 = width.

The area equation to solve becomes x(x−4)=96, or x2−4x−96=0.

To factor, find two numbers the sum to -4 and multiply to -96. -12 and 8 will work:

x2 + 8x - 12x - 96 = 0

x(x + 8) - 12(x + 8) = 0

(x - 12)(x + 8) = 0

Set each factor equal to zero and solve:

x=12 or x=−8.

Therefore the length is 12cm and the width is 8cm, giving a perimeter of 40cm.