Question

The area A of the rectangle shown is 500 square meters. Find the value of x. Then give the dimensions of the rectangle.

Answer 1

• Length=L=4x-3
• Breadth=B=2x+6

Now

• Area =LB
• (4x-3)(2x+6)=500
• 8x²+18x-518=0
• (x-7)(4x+37)=0
• x=7 or -37/4

Take it positive

• L=4(7)-3=28-3=25
• B=2(7)+6=20

Answer 2

1. Length = 4(7) - 3 = 25 m
2. Width = 2(7) + 6 = 20 m

Explanation:

Area Formula

• *Area* = *Length* × *Width*

Given

1. Area = 500 square meters
2. Length = (4x - 3) meters
3. Width = (2x + 6) meters

Solving

• (4x - 3)(2x + 6) = 500
• 8x² - 6x + 24x - 18 = 500
• 8x² + 18x - 18 - 500 = 0
• 4x² + 9x - 259 = 0
• (4x + 37)(x - 7) = 0
• x = 7 [as distance is always positive]

Dimensions

1. Length = 4(7) - 3 = 25 m
2. Width = 2(7) + 6 = 20 m