Answer:
Scale factor = 3
Step-by-step explanation:
Using similar triangles
AT/AG = AB/AC
9/3 = x+10/3x-10
Cross multiply
3(x+10) = 9(3x-10)
Expand
3x+30 = 27x-90
3x-27x = -90 - 30
-24x = -120
x = 120/24
x = 5
For the larger triangle;
AC = 3x-10
AC = 3(5)-10
AC =15-10
AC = 5
AB = x+10
AB = 5+10
AB = 15
For the scale factor;
Since AT/AG = AB/AC
9/15 = 3/5
3*3/5*3 =3/5
Since the numerator and denominator of the larger triangle is multiplies by the same factor i.3 3. Hence the scale factor is 3
x = 14
Explanation:
height = x
base 1 = 98
base 2 = 2
Using altitude formula in geometric mean:
base 1/height = height/base 2
98/x = x/2
![\begin{gathered} 196=x^2 \\ \text{square root both sides:} \\ \sqrt[]{196}\text{ = }\sqrt[]{x^2} \\ x\text{ = }\sqrt[]{196} \\ x\text{ = 14} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20196%3Dx%5E2%20%5C%5C%20%5Ctext%7Bsquare%20root%20both%20sides%3A%7D%20%5C%5C%20%5Csqrt%5B%5D%7B196%7D%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7Bx%5E2%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B196%7D%20%5C%5C%20x%5Ctext%7B%20%3D%2014%7D%20%5Cend%7Bgathered%7D)
First write the equation 8 + 12 > x because according to the triangle property, the sum of any 2 sides have to be greater than the third side. This means that the difference of any two sides should be smaller than the third side.
So, the answer would be 4 < x < 20.
Apothem = side length / 2*tan(180 / number of sides)
apothem = side length / 2*tan (180 / 7)
apothem = 6 / (2*tan(
<span>
<span>
<span>
25.7142857143</span></span></span>))
apothem = 6 / 2*0.48157
<span><span><span>apothem = 6.2296239384
</span>
</span>
</span>
Polygon area = (# of sides * side length * apothem) / 2
Polygon area = ( 7 * 6 * <span>6.2296239384) / 2
</span><span><span><span>Polygon area = 130.8221027064
</span>
</span>
</span>
