Respuesta :

semsee45

Answer:

x = 5 in

Step-by-step explanation:

Area of a rectangle = width x height

⇒ area of rectangle = 12 x 8 = 96 in²

Given shaded area = 78 in²

Area of white triangle = area of rectangle - shaded area

                                    = 96 - 78

                                    = 18 in²

Area of a triangle = 1/2 x base x height

⇒ 18 = 1/2 x 12 x height

⇒ height = 3 in

If the height of the triangle is 3 in and the height of the rectangle is 8 in

⇒ 3 + x = 8

⇒ x = 5 in

Solution:

Finding the area of the large rectangle.

[tex]Area \ of \ Large \ rectangle = LB \\\\Area \ of \ Large \ rectangle = (12)(8)\\\\ Area \ of \ Large \ rectangle = 96 \ in^{2}[/tex]

We know that:

  • [tex]"x + Height = 8 \ in."[/tex]

This means that we got two ways to find the area of the triangle.

Those methods are:

  • ⇒ [tex]Method \ 1 = \frac{1}{2} \times Base \times Height[/tex]
  • ⇒ [tex]Method \ 2 = 96 - 78[/tex]

Let's put these two methods in an equation as both are equal.

  • [tex]\frac{1}{2} \times Base \times Height = 96 - 78[/tex]

Substituting the base of the triangle:

  • [tex]\frac{1}{2} \times 12 \times Height = 96 - 78[/tex]

Simplifying the RHS:

  • [tex]\frac{1}{2} \times 12 \times Height = 18[/tex]

Simplifying the LHS:

  • [tex]6 \times Height = 18[/tex]

Dividing 6 both sides:

  • [tex]Height = \frac{18}{6} = 3 \ in[/tex]

Since the height is 3 in, the measure of x is 5 in because the sum of the height and x must be 8.

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