The Garys have a triangular pennant of area 420 in(squared)flying from the flagpole in their yard. The height of the triangle is 10 in less than 5 times the base of the triangle. What are the dimensions of the pennant?

The answer is given below:

Step-by-step explanation:

The computation of the dimension of the pennant is shown below:

As we know that

Area of the triangle = 1 ÷ 2 × base × height

where

x represents the base of the traingle

h represent the height that should be (5x - 10)

Now according to the above formula

420 =  1 ÷ 2 × x × (5x - 10)

840 = x(5x - 10)

840 = 5x^2 - 10x

5x^2 - 10x - 840 = 0

5(x^2 - 2x - 168) = 0

x^2 - 2x - 168 = 0

x^ - 14x + 12x - 168

x (x - 14) + 12(x - 14)

(x + 12) (x - 14)

So, here x = 14

Now height would be

= 5(14) - 10

= 60 inches

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.