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Joe’s rectangular garden is 6 meters long and 4 meters wide. He wishes to double the are of his garden by increasing its length and width by the same amount. Find the number of meters by which each dimension must be increased.

Respuesta :

AceCali

Answer:

ANSWER: Increase each dimension by 2 meters.

Step-by-step explanation:

L=length; W=width; X=amount of increase; A=area

.

(L+X)(W+X)=2(LW)

(6m+X)(4m+X)=2(6m)(4m)

X^2+10X+24=48

X^2+10X-24=0

(X-2)(X+12)=0

(X-2=0) OR (X+12=0)

X=2 OR X=-12

X=2 meters

abidemiokin

The dimension is increased by 2m

The formula for calculating the area of the rectangle is expressed as:

A  = lw

  • l is the length = 6m
  • w is the width = 4m

If he increases the  length and width by the same amount, the new length and width will be 6 + x and 4 + x respectively;

Substituting into the formula

2(6*4) = (6+x)(4 +x)

48 = 24 + 10x + x^2

x^2 + 10x - 24 = 0

x^2 + 12x  - 2x - 24  = 0

x(x+12) - 2(x+12) = 0

x- 2 = 0

x = 2m

This means that the dimension is increased by 2m

Learn more on area of rectangles here: https://brainly.com/question/24410768

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