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

many metres must be added to both the
length and the width to increase the area
by 750 square metres?

User Idriys
by
8.3k points

1 Answer

3 votes

Answer:

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

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

User Abracadabra
by
8.6k points

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