Question

The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?(A) 102(B) 120(C) 132(D) 144(E) 156

Answer 1

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=$90^{\circ}$

We have to find the area of triangle ABC

If angle ABC= 90 degree

From given below figure

$4a-5=2a+6$

$4a-2a=6+5$

$2a=11$

$a=\frac{11}{2}=5.5$

Substitute the values then we get

B(0,17) and C (12,17)

Distance formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB=$\sqrt{(0-0)^2+(17-0)^2}=17 units$

BC=$\sqrt{(12-0)^2+(17-17)^2}$

BC=$\sqrt{144+0}=\sqrt{144}=12$ units

Area of triangle =$\frac{1}{2}\times b\times h$

Substitute the values

Then we get

Area of triangle ABC=$\frac{1}{2}\times 17\times 12$

Area of triangle ABC=102 square units

Answer: A: 102