Question

A lot is 25 m wide and 120 m long. How

Answer 1

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:

$A_1 = 25 * 120 = 3,000~m^2$

When adding x meters to the width and the length, the new area is:

$A_2=(25+x)(120+x)$

Operating:

$A_2=x^2+145x+3,000$

We now calculate the increased area by subtracting A2-A1:

$A=x^2+145x+3,000-3,000$

$A=x^2+145x$

We are given this area is 750 square meters, thus:

$x^2+145x=750$

Rearranging:

$x^2+145x-750=0$

Factoring:

$(x-5)(x+150)=0$

Solving:

x=5, x=-150

Taking the positive solution x=5:

5 meters must be added to both the length and the width