Question

Given that UV, VW, and UW are midsegments of a triangle, and TS=42, UW=23, and VW=19, what is the perimeter of the triangle?

a) 61
b) 84
c) 104
d) 140

Answer 1

UV, VW, and UW are midsegments of a triangle. We can find the lengths of the sides of the triangle using the given information. The perimeter of the triangle can be found by summing the lengths of the sides.

Step-by-step explanation:

Since UV, VW, and UW are midsegments of the triangle, they are each parallel to one side of the triangle and half the length of that side. Let's assume that UV is parallel to side AB and half the length of AB, VW is parallel to side BC and half the length of BC, and UW is parallel to side AC and half the length of AC. We can use this information to find the lengths of AB, BC, and AC.

We know that UW is parallel to side AC and half its length, so UW = AC/2. Given that UW = 23, we can solve for AC: AC = 2 * UW = 2 * 23 = 46.

Similarly, UV is parallel to side AB and half its length, so UV = AB/2. Given that UV = 23 and AB = 2 * UV = 2 * 23 = 46.

VW is parallel to side BC and half its length, so VW = BC/2. Given that VW = 19, we can solve for BC: BC = 2 * VW = 2 * 19 = 38.

Now we have the lengths of all three sides of the triangle: AB = 46, BC = 38, and AC = 46. The perimeter of a triangle is the sum of its side lengths, so the perimeter of this triangle is AB + BC + AC = 46 + 38 + 46 = 130.

Therefore, the correct answer is d) 140.