SAT question

• Jun 26th 2012, 11:12 AM
zambo34
SAT question
3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I 24
II 20
III 5
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

the correct answer is D i and get II 20 but not III 5

sorry repost i put it in the wrong section earlier.
• Jun 26th 2012, 11:30 AM
earboth
Re: SAT question
Quote:

Originally Posted by zambo34
3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I 24
II 20
III 5
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

the correct answer is D i and get II 20 but not III 5

sorry repost i put it in the wrong section earlier.

Actually the area of the triangle can be 20 as it's maximum and 0 at it's minimum.

In the attachment you can see a triangle with it's base of 5 and it's height of 2. Thus it's area has the value 5.
• Jun 26th 2012, 11:58 AM
richard1234
Re: SAT question
Another way to think of it: Let $\theta$ be the angle between the two sides of lengths 8 and 5. The area of the triangle is $\frac{1}{2}*8*5*\sin \theta = 20 \sin \theta$

Since $\sin \theta$ ranges between 0 and 1 (for $0 \le \theta \le \pi$), the area can range from 0 to 20. The correct answer is D.

Note: You don't need​ trig on the SAT, but you can definitely use it.