Write an equation

Question

Write an equation to represent the question that follows. Then solve the equation. In △TUV, ∠T is a right angle. TU = 10, UV = 26, and VT = 24. If △TUV ∼ △WXY and WY = 72, what is the area of △WXY?

Answer 1

Hello, take a look below:

Recall that the area of a triangle is A = 1/2 base x height. We have right triangles here, so the legs of our triangles are the base and height no matter how you draw your triangle.

Which segments of triangle TUV are the legs, or base and height? Remember that in a right triangle, the hypotenuse is the LONGEST line segment in triangle. With that information, we see that UV = 26 is the longest part of TUV. Thus, TU = 10 and VT = 24 are the legs of the triangle.

Triangle TUV and triangle WXY are similar. Since they are similar, the segments WY and TV are similar (TV is written as VT in the problem). If VT = 24 and WY = 72, then triangle WXY is three times as big as triangle TUV. Thus, TU = 10 means that WX must equal 30.

WX = 30 and WY = 72 and these are your base and height.

Area = 1/2 bh

A = 1/2 (30)(72)

A = 1080 units squared