Answer:
A:102
Step-by-step explanation:
We are given that the points A(0,0),B(0,4a-5) and C(2a-+1,2a+6) form a triangle.
If angle ABC=[tex]90^{\circ}[/tex]
We have to find the area of triangle ABC
If angle ABC= 90 degree
From given below figure
[tex]4a-5=2a+6[/tex]
[tex]4a-2a=6+5[/tex]
[tex]2a=11[/tex]
[tex]a=\frac{11}{2}=5.5[/tex]
Substitute the values then we get
B(0,17) and C (12,17)
Distance formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB=[tex]\sqrt{(0-0)^2+(17-0)^2}=17 units[/tex]
BC=[tex]\sqrt{(12-0)^2+(17-17)^2}[/tex]
BC=[tex]\sqrt{144+0}=\sqrt{144}=12[/tex] units
Area of triangle =[tex]\frac{1}{2}\times b\times h[/tex]
Substitute the values
Then we get
Area of triangle ABC=[tex]\frac{1}{2}\times 17\times 12[/tex]
Area of triangle ABC=102 square units
Answer: A: 102
