Mathematics: 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

Step-by-step explanation:n sped...

The points a(0, 0), b(0, 4a - 5) and c(2a + 1, 2a

hernandezaniyah660

01.01.2022

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

A: 102

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