How wide is the river?

Question

Charmaine wants to measure the width of a river. She marks off two right triangles, as shown in the figure. The base of the larger triangle has a length of 61m, and the base of the smaller triangle has a length of 31m. The height of the smaller triangle is 23.4m. How wide is the river? Round your answer to the nearest meter. (The figure is not drawn to scale.)

Answer 1

Let's suppose the drawing can be described as follows:

 

The large right triangle is inside the river, with its base along a side of the river, and its height is across the width of the river.

The small right triangle is outside the river, with its base along the same side of the river.

There is no overlap of triangles. An endpoint of their bases touch, and an endpoint of their hypotenuses touch.

If this doesn't match your drawing, stop now. (-:

 

We have 2 similar triangles, where the ratios of the corresponding sides are equal. That is, h1/b1 = h2/b2

 

Here, h1 is the height of the large triangle (the width of the river)

h1/61 = 23.4/31

h1 = 23.4/31 * 61 = approx 46 m