How is this a right angle triangle

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What is the area of a triangle created by the intersections of the lines x=4, y=5, and y=−3/4x+20?


42


54


66


72


96

[[email protected]]

Hi shibsriz,

I'm going to offer a quick run-down of the "steps" to solve this problem so that you can attempt them on your own:

If you graph the 3 lines that are defined in this question, you'll end of up with a triangle. In addition, you know that it MUST be a right triangle because one line is horizontal (Y = 5) and one is vertical (X = 4). When a horizontal line and a vertical line "criss-cross", you end up with a 90 degree angle.

By graphing the third line: Y = (-3/4)X + 20, you'll have a diagonal line that completes the triangle. This line will help you calculate the base and the height, so you can calculate the area of the triangle.

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

I've added some brackets to the 3rd equation to show the intent of the question.

What is the area of a triangle created by the intersections of the lines x = 4, y = 5, and y = (−3/4)x + 20?

A) 42
B) 54
C) 66
D) 72
E) 96

Let's first sketch the lines x = 4 and y = 5


To find the point where y = (-3/4)x + 20 intersects the line x = 4, replace x with 4 to get: y = (-3/4)4 + 20 = 17
So the point of intersection is (4, 17)

To find the point where y = (-3/4)x + 20 intersects the line y = 5, replace y with 5 to get: 5 = (-3/4)x + 20
When we solve for x, we get x = 20
So the point of intersection is (20, 5)

Add this information to our sketch:


From here, we can determine the length of the right triangle's base and height:


Area = (1/2)(base)(height)
= (1/2)(16)(12)
= [spoiler]96 = E [/spoiler]

Cheers,
Brent

[GMATinsight]

What is the area of a triangle created by the intersections of the lines x=4, y=5, and y=-3/4x+20?


42


54


66


72


96

In the equation y=-3/4x+20
@x = 4, y = 17
@y = 5, x = 20

Therefore base of the triangle is 20-4 = 16
Height of Triangle = 17-5 = 12

Area = (1/2) Base x Height = (1/2) x 12 x 16 =[spoiler]96 Option E[/spoiler]