Question

3. The area of a small rectangular plot is 88 m. If the difference between its length and its breadth is 3 cm, find
its perimeter.....pls explain with a diagram..if possible!!!​

Answer 1

Correction in the question: The area of a small rectangular plot is 88m². If the difference between its length and its breadth is 3m, find  its perimeter.

The difference is in meters and not centimetres as the length and breadth we get when it's solved using 3cm as the difference will not give us 88m² as the area.

Answer:

Perimeter is 38 metres.

Step-by-step explanation:

Given:

Area of the rectangular plot = 88m²

Length - Breadth = 3m.

➝ l - b = 3m → Eq(1)

To find:

The perimeter.

Solution:

ATQ, Area of the rectangular plot is 88m².

➝ Area of the rectangular plot = 88m²

➝ Length × Breadth = 88m²

➝ l × b = 88m²

➝ [3 + b] × b = 88m²

➝ 3b + b² = 88m²

➝ b² + 3b - 88 = 0

➝ b² + 3b - 88 = 0

➝ b² + 11b - 8b - 88 = 0

➝ b(b + 11) - 8(b + 11) = 0

➝ (b + 11)(b - 8) = 0

Therefore:

➝ b + 11 = 0

➝ b = -11

Breath/measurements can't be negative.

∴ Breadth is not equal to -11m.

➝ b - 8 = 0

➝ b = 8

∴ Breadth is equal to 8m.

Substitute the value of "b" in Eq(1).

➝ l - b = 3

➝ l - 8 = 3

➝ l = 3 + 8

➝ l = 11

∴ Length is equal to 11m.

Now, the perimeter of the rectangle = 2(Length + Breadth)

➝ Perimeter of the rectangle = 2(Length + Breadth)

➝ Perimeter of the rectangle = 2(11 + 8)

➝ Perimeter of the rectangle = 2(19)

➝ Perimeter of the rectangle = 38m.

Answer 2

Answer:

given area = 88m square

difference between length and it's bredth = 3m

let length and breadth be x and y

then

area xy = 88m square (1)

x -y = 3m

then x = y+3

put x value in (1)

then y(y+3) = 88

$y {}^{2} + 3y = 88$

$y {}^{2} + 3y - 88 = 0$

$y {}^{2} + 11y - 8y - 88 = 0$

$y(y + 11) - 8(y + 11) = 0$

$(y + 11)(y - 8) = 0$

y = 8 or y = -11

x-y =3

x-8 = 3

x = 11

perimeter = 2(l+b) = 2(11+8)

2(19) = 38 meters