sandy wrote:
Attachment:
#GREpracticequestion The area of triangle PQR.jpg
Quantity A |
Quantity B |
The area of triangle PQR |
The area of triangle PSR |
Quantity A is pretty straightforward since we are given the lengths of the two legs.
So one leg can be the base, and the other leg can be the height.
Area of triangle = (base)(height)/2= (2√5)(√5)/2
= 10/2
= 5
So the area of triangle PQR = 5
In order to find the area of triangle PSR (Quantity B), we must first find the lengths of the two missing sides: side PR and side PS
Let's first find the length of side PR
Let's
let x = the length of side PRSince the red triangle (highlighted above) is a RIGHT triangle, we can apply the Pythagorean theorem to write: (2√5)² + (√5)² = x²
Simplify to get: 20 + 5 = x²
Simplify again: 25 = x²
Solve: x = 5 or x = -5
Since lengths cannot be negative, we can be certain that x = 5
In other words, the length of side PR =
5, which we'll add to the diagram below

At this point we need to find the length of side PS.
Since we already know that two sides have lengths 3 and 5, we might recognize that those lengths are part of the 3-4-5 Pythagorean Triplet, which means the missing side must have length
4We get:

Now that we have all of the necessary lengths, we can find the area of a triangle PSR (Quantity B)
Area of triangle = (base)(height)/2= (4)(3)/2
= 6
So the area of triangle PSR = 6
We get:
QUANTITY A: 5
QUANTITY B: 6
Answer: B
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep