Question

A rectangular pond has a length of 4 m more than twice its width. Solve for the length and the width if the area of the said pond is 96m^2

Answer 1

Given

• Rectangular pond has a length of 4m more than twice of its width.
• Area of the rectangular pond = 96m²

To find

• Length and breadth of the rectangular pond.

Figure

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Solution

→ Let the breadth of the rectangle be x m

Then, length = (2x + 4)m

$\boxed{\underline{Area\: of\: a\: rectangle = l × b}}$

→ l × b = 96

→ (2x + 4) × x = 96

→ 2x² + 4x = 96

→ 2x² + 4x - 96 = 0

By Factorising...

→ 2x² + 16x - 12x - 96 = 0

→ 2x(x + 8) -12(x + 8) = 0

→ (x + 8) (2x - 12) = 0

→ x = -8 [this is not possible because breadth can't be negative]

→ x = 6

Hence, breadth of the pond is 6m

Now,

★ Length = (2x +4)m = 2 × 6 + 4

★ Length = 16m

Answer 2

Solution :-

Let us assume that, width of the rectangular pond is equal to x m .

So,

→ Length of rectangular pond = 4 more than twice of width = (2x + 4) m

then,

→ Area of rectangular pond = Length * Width

A/q,

→ (2x + 4) * x = 96

→ 2(x + 2) * x = 96

dividing both sides by 2,

→ (x + 2) * x = 48

→ x² + 2x = 48

→ x² + 2x - 48 = 0

→ x² + 8x - 6x - 48 = 0

→ x(x + 8) -6(x + 8) = 0

→ (x + 8)(x - 6) = 0

putting both equals to zero,

→ x = (-8) m or 6 m .

since length of width cant be a negative value .

Therefore,

→ Width of rectangular pond = x = 6 m

→ Length of rectangular pond = (2x + 4) = 2 * 6 + 4 = 12 + 4 = 16 m

Hence, the length and the width of rectangular pond are 16m and 6m respectively .

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