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Joe has a rectangular patio that measures 10 feet by 12 feet. he wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. which equation could be used to determine x?

Respuesta :

calculista
we know that

step 1
find the original area of rectangle

Area of rectangle=L*W-----> 10*12----> 120 ft²

step 2
find the new area
if increase the area by 50%
so 
the new area=120*1.5----> 180 ft²

step 3
find the new dimensions
(10+x) ft x (12+x) ft
new area=(10+x)*(12+x)
180=(10+x)*(12+x)----> 180=120+10x+12x+x²----> 180=x²+22x+120
x²+22x-60=0

using  a graph tool-----> to resolve the second order equation
see the attached figure
the solution is
x=2.454 ft

the answer 
the equation is
[tex] x^{2} +22x-60=0[/tex]
Ver imagen calculista

The area of the rectangle which is increased by 50% is given by the equation will be x² + 22x - 60 = 0.

What is a rectangle?

The area of a rectangle is the product of its length and width.

If a rectangle has a length of L units and a width of W units, then

Area = L × W squared units.

Joe has a rectangular patio that measures 10 feet by 12 feet.

He wants to increase the area by 50% and plans to increase each dimension by equal lengths (x).

Then the dimension of the rectangular patio will be

L = (12 + x)

W = (10 + x)

A = 10 × 12 = 120 square feet

If the area of the rectangular patio is increased by 50%. Then the area will be

A = 120 × 1.5 = 180 square feet

Then we have

              L × W = Area

(12 + x)(10 + x) = 180

120 + 22x + x² = 180

 x² + 22x - 60 = 0

More about the rectangle link is given below.

https://brainly.com/question/10046743

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