Arectangle is 6 meters longer than it is wide. the area of the rectangle is 315 square meters. find the length

The length is 21 meters

Step-by-step explanation:

* Lets use variable to represent the dimensions of the rectangle

- The length of the rectangle is 6 meters longer than its width

# Let the width of the rectangle = x meters

∴ The length of the rectangle = x + 6 meters

- The area of the rectangle = Length × width

∵ The area of the rectangle = 315 meters²

∵ The length of the rectangle = x + 6

∵ The width of the rectangle = x

∴ x(x + 6) = 315 ⇒ open the brackets to solve the equation

∴ x² + 6x = 315 ⇒ subtract 315 from both sides

∴ x² + 6x - 315 = 0

- Lets factorize the quadratic equation to find the value of x

∵ The last term of the quadratic is negative

∴ The brackets have different sign

# x² = x × x ⇒ 1st terms in the two brackets

# -315 = -15 × 21 ⇒ 2nd terms in the two brackets

# x × -15 = -15x ⇒ 1st term in the first bracket and 2nd term in

  the second bracket

# x × 21 = 21x ⇒ 1st term in the second bracket and 2nd term

  in the first bracket

# 21x - 15 x = 6x ⇒ the middle term of the quadratic equation

∴ The factoriz of x² + 6x - 315 = 0 is

  (x + 21)(x - 15) = 0

∴ x + 21 = 0 OR x - 15 = 0

# x + 21 = 0 ⇒ subtract 21 from both sides

∴ x = -21 ⇒ neglect this answer because there is no negative

  value for the dimensions

# x - 15 = 0 ⇒ add 15 to both sides

∴ x = 15

- The value of the width is x

∴ The width = 15 meters

- The value of the length is x + 6

∴ The length = 15 + 6 = 21 meters

2 is the final ! : )

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step-by-step explanation: