Answer:
5 meters must be added to both the length and the width
Step-by-step explanation:
Area of a Rectangle
A rectangle of width W and length L has an area calculated as:
A = W*L
Initially, the lot has a width of W1=25 m and a length of L1 = 120 m, thus its area is:
[tex]A_1 = 25 * 120 = 3,000~m^2[/tex]
When adding x meters to the width and the length, the new area is:
[tex]A_2=(25+x)(120+x)[/tex]
Operating:
[tex]A_2=x^2+145x+3,000[/tex]
We now calculate the increased area by subtracting A2-A1:
[tex]A=x^2+145x+3,000-3,000[/tex]
[tex]A=x^2+145x[/tex]
We are given this area is 750 square meters, thus:
[tex]x^2+145x=750[/tex]
Rearranging:
[tex]x^2+145x-750=0[/tex]
Factoring:
[tex](x-5)(x+150)=0[/tex]
Solving:
x=5, x=-150
Taking the positive solution x=5:
5 meters must be added to both the length and the width
