What is the area of a triangle (easier solution)

[melguy]

Please help with the problem. Thanks

[ganeshrkamath]

Please help with the problem. Thanks

x=4_________(1)
y=5_________(2)
y = (-3/4)x + 20_________(3)

Put (1) in (3): y = -3 + 20 = 17
Point A = (4,17)

Put (2) in (3): 5 = (-3/4)x + 20
(3/4)x = 15
x = 20
Point B = (20,5)

Point C = (4,5)

From figure, it is clear that the the triangle is a right angled triangle with the right angle at C.
BC = 20 - 4 = 16
AC = 17 - 5 = 12

Area = 1/2 * 16 * 12 = 96

Choose E

Cheers

PS : This might look like a long solution, but you will realize it's actually small when you work it out.

[Brent@GMATPrepNow]

Original question:





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)
= 96
= E

Cheers,
Brent

[melguy]

Thanks both of you for your help!

Brent - you mentioned about posting the image within the question. I am not sure how can i do it?

[Brent@GMATPrepNow]

Thanks both of you for your help!

Brent - you mentioned about posting the image within the question. I am not sure how can i do it?

Hey melguy,

Use the "add image" option. This, I believe, makes the image viewable for those logged in and for those not.

So, how many more days until your test?

Cheers,
Brent

[melguy]

Thanks!

My test is on 10th Sep

[Brent@GMATPrepNow]

I predict great things!

Cheers,
Brent

[melguy]

Thanks a lot Brent