Question

Using the triangle, find the length of the river

Answer 1

17 m

Explanation:

Two right triangles are shown.

Let the width of the triangle = x.

Smaller triangle:

Vertical leg: 8 m

Horizontal leg: 7 m + x + 8 m = x + 15m

Larger triangle:

Vertical leg: 15 m

Horizontal leg: 28 m + 7 m + x + 8 m = x + 43 m

The triangles are similar, so the lengths of corresponding sides are proportional.

15/8 = (x + 43)/(x + 15)

8(x + 43) = 15(x + 15)

8x + 344 = 15x + 225

-7x = -119

x = 17

Answer: 17 m

Answer 2

17 m

Explanation:

Given similar triangles, and the width of a river making up part of one side, you want to find the width of the river.

Similar triangles

Here, it is convenient to divide the trapezoid on the left into a rectangle 8 m high and 28 m wide, and a triangle 7 m high and 28 m wide. This shows us the width of the triangle is 28/7 = 4 times its height.

That means the triangle on the right will have a total width that is 4 times its height: 4×8 m = 32 m.

That 32 m width is made up of three parts:

7 m + river width + 8 m = 32 m

river width = 17 m . . . . . . . . . . . . subtract 15 m

The width of the Braady River is 17 m.

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Additional comment

Referencing the named points in the attached figure, the left trapezoid is ABDE, and the triangle of interest there is AFE.

That triangle and the triangle on the right, EDC, are similar, so corresponding side ratios are the same: EF/FA = CD/DE.

Then CD = DE(EF/FA) = 8(28/7) = 32, as above.