If vertices of a triangle are A (5, 0), B (x, y)

[Asma77]

If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?


(1) |x| = y = 10

(2) x = |y| = 10

Dear GMATGuruNYexpert, I need to understand by drawing how statement 1 is suff

I used this formula X1(Y2-Y3)+X2(Y3-Y1)+X3(Y1-Y2)/2 to find the triangle area and the answer was D

but i really confused when i tried to draw statement 1 especially in the case x,y=(-10, 10) i do not

know how to get the height equal to 10 In the green triangle I need to

understand which side is the height and how it equal to 10.I really confused Sad Sad Sad

[GMATGuruNY]

A height extends from a vertex to form a RIGHT ANGLE with the opposite side.



In ∆ABC, if AC is considered the base, then BE is the corresponding height.
Since AC=20 and BE=10, area = (1/2)(20)(10) = 100.

In ∆ADC, if AC is considered the base, then DF is the corresponding height.
Since AC=20 and DF=10, area = (1/2)(20)(10) = 100.

Since the area is the same in each case, statement 1 is SUFFICIENT.

[Brent@GMATPrepNow]

If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

(1) |x| = y = 10
(2) x = |y| = 10

ASIDE: For statement 1, notice that the length of the BASE (AC) is already fixed at 20.
Since the base is on the x-axis, the HEIGHT of the triangle will be the y-coordinate of point B.
Statement 1 tells us that the y-coordinate of point B is 10.
So, if we place point B ANYWHERE on the line y = 10, the HEIGHT of the triangle will equal 10.
Area = (1/2)(base)(height)
= (1/2)(20)(10)
= 100

Cheers,
Brent

[Matt@VeritasPrep]

i do not know how to get the height equal to 10 in the green triangle

Good news: the height does not actually have to be inside the triangle! If you choose the side on the x-axis to be the base of the triangle, the height is just the distance from the x-axis to the top vertex of the triangle. Since the top vertex has a y-value of 10 and the x-axis has a y-value of 0, your height = 10, and you're set!