Question

The length of a rectangle is 12 meters greater than twice the width. Its area is 32 sq. meters. Find the dimensions of the rectangle.

Answer 1

ANSWER :

• ❖ If the length of a rectangle is 12 meters greater than twice the width. Its area is 32 sq. meters; then the dimensions of the rectangle will be :- Length = 16 meters, Width = 2 meters.

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SOLUTION :

❒ Given :-

• The length of the rectangle is 12 meters greater than twice the width.

• Area of the rectangle is 32 sq. meters

❒ To Find :-

• Dimension of the rectangle = ?

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❒ Calculation :-

Suppose,

• Length of the rectangle = p meters

• Width of the rectangle = q meters

It is given that,

• The length of the rectangle is 12 meters greater than twice the width.

∴ p = 2q+ 12 ----------> (1)

We know that,

• $\dag \: \: \underline{ \boxed{ \sf{ \: Area \: \: of \: \: a \: \: rectangle = Length \times Width \: }}}$

It is given that,

• Area of the rectangle is 32 sq. meters.

Using the formula of the Area of rectangle, we get,

• ✎ Length × Width = Area of the rectangle

∴ p × q = 32 ----------> (2)

Substituting the value of p from eq. (1) in eq. (2), we get,

• ★ p × q = 32

⇒ (2q + 12) × q = 32

⇒ 2q² + 12q = 32

⇒ 2q² + 12q - 32 = 0

Taking 2 as common, we get,

• ★ 2q² + 12q - 32 = 0

⇒ 2 ( q² + 6q - 16) = 0

⇒ q² + 6q - 16 = 0

Splitting middle term of the equation, we get,

• ★ q² + 6q - 16 = 0

⇒ q² + (8 - 2)q - 16 = 0

⇒ q² + 8q - 2q - 16 = 0

⇒ q (q + 8) - 2 (q + 8) = 0

⇒ (q + 8) (q - 2) = 0

So,

• q + 8 = 0

➨ q = - 8

or,

• q - 2 = 0

➨ q = 2

As q is the width of the rectangle, it can not be a negative number.

Here,

• q ≠ - 8

∴ q = 2

Substituting the value of q in eq. (1), we get,

• ✪ p = 2q+ 12

➨ p = 2 × 2 + 12

➨ p = 4 + 12

∴ p = 16

Thus, Dimension of the rectangle is :-

• Length = p meters = 16 meters.

• Width = q meters = 2 meters.

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KNOW MORE :

➤ Rectangle :-

• ✎ A rectangle is a plane figure which has four sides and four angles. Each of the four angles are right angles, i.e, 90°. Again, the opposite sides of a rectangle are of equal length and parallel.

• ✎ A rectangle is or a quadrilateral which opposite sides are equal and parallel to each other and each of the four angles is a right angle.

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➤ Related Formulas :-

• ✎ Area of a rectangle = Length × Width

• ✎ Perimeter of a rectangle = 2 (Length + Width)

• ✎ Diagonal of a rectangle = √{(Length)² + (Width)²}

Answer 2

Answer:

is attached

Step-by-step explanation:

i hope this helps u