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Help me plz. The sides of a rectangular terrain are given by the expressions (x - 5) y
(x – 7) meters. Determine an algebraic expression that represents its area.
Once the expression is obtained, what are the measures of the terrain, so its
area is 195 m² ? What is the perimeter of the terrain?

Respuesta :

7492

Area = (x - 5)(x – 7)

Area = x(x - 7) - 5(x - 7)

Area = x^2 -7x -5x + 35

Area = x^2 -12x + 35

algebraic expression that represents its area: x^2 -12x + 35

x^2 - 12x + 35 = 195

x^2 - 12x + 35 - 195 = 0

x^2 - 12x - 160 = 0

x^2 - 8x - 20x - 160 = 0

x (x + 8) - 20 (x + 8) = 0

(x + 8) (x - 20) = 0

(x + 8) = 0

(x - 20) = 0

x = - 8 (not a solution)

x = 20

hence,

length = x - 5

length = 20 - 5

length = 15 m

width = x - 7

width = 20 - 7

width = 13 m

perimeter = 2(13) + 2(15)

perimeter = 26 + 30

perimeter = 56 m²

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