WHEN IS THE WEBINAR?

Did you know that Target Test Prep and Beat the GMAT are hosting a webinar sometime in August? The webinar starts at 12:00 PM Eastern Time…but ==on what day?== Solve the geometry problem below to find out!

✎ Solution:

Notice that the corresponding angle measurements in one triangle are equal to those of the other triangle. Thus, ΔTRG and ΔBTG are similar triangles and their corresponding side lengths will be proportional.

We are given lengths of two sides of ΔTRG and one side of ΔBTG, so let’s see if we can find the ratio of the given side lengths of one triangle to the other.

Since ∠TGR is equal to ∠GBT, the length of the side opposite ∠TGR corresponds to the length of the side opposite ∠GBT.

⇒ ∠TGR = ∠GBT = 50°

The side opposite the 50° angle in ΔTRG is side TR and the side opposite the 50° angle in ΔBTG is side GT. We can now find the ratio of the side lengths of the two similar triangles.

⇒ TR/GT = 8/4 = 2

Since TR/GT = 2, the ratio of the side lengths of ΔTRG to the side lengths of ΔBTG is 2:1, or 2/1. Using the ratio of the sides of ΔTRG to those of ΔBTG, we can now solve for the length of side BT.

⇒ 2/1 = RG/BT → 2/1 = 6/BT

→ 2BT = 6

→ BT = 6/2

→ BT = 3

Now that we know the length of side BT, we know the lengths of both legs of ΔBTG. Since GT = 4, BT = 3, and ΔBTG is a right triangle, ΔBTG must be a
3—4—5 right triangle. Thus, w = 5.

Since w = 5, Target Test Prep and Beat the GMAT will hold their webinar on August 5th, 2015. (at 12:00 PM Eastern!)