singhsa wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

A. I ONLY
B. 1 AND II ONLY
C. I AND III ONLY
D. II AND III ONLY
E. I,II AND III ONLY.


Here, the third side can obviously be b/w 4 and 20.

oa - b

GMATGuruNY wrote:

singhsa wrote:If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle?

I 35
II 48
III 56

A. I ONLY
B. 1 AND II ONLY
C. I AND III ONLY
D. II AND III ONLY
E. I,II AND III ONLY.


answer is d

GMATGuruNY wrote:
When given 2 sides of a triangle, we'll get the largest possible area if we make one of the known sides the base and the other known side the height, placing a right angle between them.

Let's say we make 12 the base and 8 the height with a right angle between them. A = 1/2 * 12 * 8 = 48.

If we then change the angle between the two sides so that it's larger or smaller than 90 degrees, the base will remain 12 but the height will be become smaller than 8. Since a smaller height will yield a smaller area, 48 is the largest area possible.

Eliminate C, D and E because they each include 56 as a possible area.
Eliminate A because it doesn't include 48 as a possible area.

The correct answer is B.

singhsa wrote:

GMATGuruNY wrote:
When given 2 sides of a triangle, we'll get the largest possible area if we make one of the known sides the base and the other known side the height, placing a right angle between them.

Let's say we make 12 the base and 8 the height with a right angle between them. A = 1/2 * 12 * 8 = 48.

If we then change the angle between the two sides so that it's larger or smaller than 90 degrees, the base will remain 12 but the height will be become smaller than 8. Since a smaller height will yield a smaller area, 48 is the largest area possible.

Eliminate C, D and E because they each include 56 as a possible area.
Eliminate A because it doesn't include 48 as a possible area.

The correct answer is B.

Hey,

I am getting one thing here. We are considering a triangle with a base of 12 and a height of 8. But we're not given the third side. How can we assume the third side to be a hypotenuse.

From the properties of triangles, we know that the third side can only be b/w 4 and 20. So, what if the third side is 10. Won't the area of triangle then become 1/2 * 12*10=60 ?

GMATGuruNY wrote:

singhsa wrote:

GMATGuruNY wrote:
When given 2 sides of a triangle, we'll get the largest possible area if we make one of the known sides the base and the other known side the height, placing a right angle between them.

Let's say we make 12 the base and 8 the height with a right angle between them. A = 1/2 * 12 * 8 = 48.

If we then change the angle between the two sides so that it's larger or smaller than 90 degrees, the base will remain 12 but the height will be become smaller than 8. Since a smaller height will yield a smaller area, 48 is the largest area possible.

Eliminate C, D and E because they each include 56 as a possible area.
Eliminate A because it doesn't include 48 as a possible area.

The correct answer is B.

Hey,

I am getting one thing here. We are considering a triangle with a base of 12 and a height of 8. But we're not given the third side. How can we assume the third side to be a hypotenuse.

From the properties of triangles, we know that the third side can only be b/w 4 and 20. So, what if the third side is 10. Won't the area of triangle then become 1/2 * 12*10=60 ?

If the 3rd side = 10, the area will be smaller than 48 because the base will remain the same while the height becomes smaller.

Please see the attachment, which illustrates why the largest possible area will be achieved if the 2 given sides form the base and the height. Any other configuration will yield a smaller area because the height will become smaller.

lokesh r wrote:

GMATGuruNY wrote:

singhsa wrote:

GMATGuruNY wrote:
When given 2 sides of a triangle, we'll get the largest possible area if we make one of the known sides the base and the other known side the height, placing a right angle between them.

Let's say we make 12 the base and 8 the height with a right angle between them. A = 1/2 * 12 * 8 = 48.

If we then change the angle between the two sides so that it's larger or smaller than 90 degrees, the base will remain 12 but the height will be become smaller than 8. Since a smaller height will yield a smaller area, 48 is the largest area possible.

Eliminate C, D and E because they each include 56 as a possible area.
Eliminate A because it doesn't include 48 as a possible area.

The correct answer is B.

Hey,

I am getting one thing here. We are considering a triangle with a base of 12 and a height of 8. But we're not given the third side. How can we assume the third side to be a hypotenuse.

From the properties of triangles, we know that the third side can only be b/w 4 and 20. So, what if the third side is 10. Won't the area of triangle then become 1/2 * 12*10=60 ?

If the 3rd side = 10, the area will be smaller than 48 because the base will remain the same while the height becomes smaller.

Please see the attachment, which illustrates why the largest possible area will be achieved if the 2 given sides form the base and the height. Any other configuration will yield a smaller area because the height will become smaller.

since third side can be anything b/w 4 and 20 exclusive.

how can i say area of triangle will be <48 , if say base is 19?

frank1 wrote:You showed how the area couldnot be greater than 48 so 56 is out
but
You didn't show why 35 could not be the area.As the question doesnt explicitly says the sides could not be in decimal point
i can see that area can be 35 as well....
any reason for that...