This video contains GMAT Math Review of Rectangle. Watch it and review the properties of the rectangle to help you on the GMAT Math Section.
GMAT Math Review of Rectangle [Video Transcript]
Please pause this video and answer the question before continuing.
Now, in this question, we want to find the height of the rectangle. Let’s begin by adding the given information to our diagram. First we’re told that this is a rectangle. So we can add these to the note that we have 90 degree angles at the four corners. Next we’re told that the height is twice the width. Now, since we’re not given any measurements concerning the height and width, let’s assign some variables. If we let X equal the width of the rectangle, then the height must be two X, since the height is twice the width. Finally we’re told that the distance from point A to point B is root 60. So let’s add this information to our diagram.
Okay, that’s all of the given information, now we want to find the value of two X, the rectangle’s height. At this point we should recognize that within this diagram we have a right triangle hiding. Since this is a right triangle, we can apply the Pythagorean Theorem that relates the three sides. So if we square both legs and add them together, the sum will be equal to the square of the hypotenuse. We now have an equation that we can solve for X. First we can expand two X to the power of two to be four x squared. And next we can evaluate root 60 to the power of two, which is 60. From here we can simplify the left hand side, and now we can divide both sides by five.
Now, if X squared is equal to 12, then X must equal the square root of 12. At this point, we can simplify the square root of 12 by first re-writing it as root four times root three. And now we can replace root four with two, to see that X is equal to two root three. Now, be careful. We’re not done just yet. The question asks us to find the height of the rectangle and X represents the width. To find the height, we must multiple X by two to get two times two root three, which is equal to four root three. So the answer here is D.