Answer:
The length is 21 meters
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