Thread: 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.

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.

Another way to think of it: Let be the angle between the two sides of lengths 8 and 5. The area of the triangle is


Since ranges between 0 and 1 (for ), 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.