1. **Problem statement:** Find the width of the Brady River given a trapezoidal shape with vertical segment 15 m, horizontal segment 28 m, and sides 7 m and 8 m. 2. **Formula and approach:** The width of the river corresponds to the length of the segment perpendicular to the riverbanks. We can use the Pythagorean theorem or trapezoid properties to find the missing width. 3. **Step-by-step solution:** - The trapezoid has two parallel sides: one side is 28 m (bottom), and the other side is unknown (top width). The two non-parallel sides are 7 m and 8 m. - The vertical height between the parallel sides is 15 m. - We can drop perpendiculars from the top side to the bottom side to form right triangles. - Let the top width be $x$. - The difference between the bottom and top widths is $28 - x$. - The two right triangles formed have legs 15 m (height) and bases $a$ and $b$ such that $a + x + b = 28$. - The sides 7 m and 8 m are the hypotenuses of these right triangles, so: $$a^2 + 15^2 = 7^2 \Rightarrow a^2 + 225 = 49 \Rightarrow a^2 = 49 - 225 = -176$$ This is impossible, so the 7 m and 8 m sides must be the legs, not hypotenuses. - Instead, assume the 7 m and 8 m sides are the legs perpendicular to the 28 m base. - The width is then the sum of the vertical segment 15 m plus the horizontal segments 7 m and 8 m. - Therefore, the width is: $$15 + 7 + 8 = 30$$ 4. **Answer:** The width of the Brady River is 30 meters.