Question

A rectangle's width is 6 feet less than its length. If the area of the rectangle is 247 square feet, what is its length, in feet?

Answer 1

Answer:

Lets the length be x and the breadth be x- 6 respectively,

Area of the triangle = 247square feet

L×B = 247

x× x-6 = 247

2x- 6 = 247

2x = 247+6

2x = 253

x = 253/2

x = 126.5

Therefore, length = 126.5

Breadth= 126.5-6

= 120.5

Answer 2

Given :

A rectangle's width is 6 feet less than its length. If the area of the rectangle is 247 square feet.

To Find :

The length in feet.

Solution :

Analysis :

Here the formula of area of rectangle is used. We can see that the length and breadth both are dependent on each other. So we have to form equation through which we can find the length.

Required Formula :

Area of rectangle = Length × breadth

Explanation :

Let us assume that the length is "x" ft.

Breadth = "x - 6" ft.

• Area = 247 ft²

We know that if we are given the area of the rectangle and is asked to find the length and breadth of the rectangle,

Area of rectangle = Length × breadth

where,

• Area = 247 ft²
• Length = x ft
• Breadth = x - 6 ft

Using the required formula and substituting the required values,

⇒ Area of rectangle = Length × breadth

⇒ 247 = x × (x - 6)

Expanding the brackets,

⇒ 247 = x² - 6x

⇒ 0 = x² - 6x - 247

⇒ x² - 6x - 247 = 0

Splitting the middle term,

⇒ x² + 13x - 19x - 247 = 0

⇒ x(x + 13) - 19(x + 13) = 0

⇒ (x - 19)(x + 13) = 0

⇒ (x - 19) = 0

⇒ x - 19 = 0

⇒ x = 19

∴ x = 19.

⇒ (x + 13) = 0

⇒ x + 13 = 0

⇒ x = -13

∴ x = -13.

Dimensions cannot have negative value so we will neglect -13 as one the dimensions.

Considering 19 as one of the dimensions,

The dimensions :

• Length = x = 19 ft
• Breadth = x - 6 = 19 - 6 = 13 ft

The length of the rectangle is 19 feet.

Verification :

⇒ Area of rectangle = Length × breadth

⇒ 247 = 19 × 13

⇒ 247 = 247

∴ LHS = RHS.

• Hence verified.