Question

A huge forest has a fence on the shape of a right triangle with sides measuring 850 radical 3 miles, 850 miles, and 1700 miles. During the winter season, the forest rangers open up another road to bypass the snow that could accumulate. The road will connect the right angle of the forest to the hypotenuse. Determine the shortest possible length for the bypass road.

Answer 1

Answer:

The shortest possible length for the bypass road is 1,275 miles

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem triangles ABC and CDB are similar by AA Similarity Theorem

so

$\frac{BC}{DB}=\frac{AC}{CB}$

substitute the given values

$\frac{850\sqrt{3}}{DB}=\frac{1,700}{850\sqrt{3}}$

solve for DB

$DB=({850\sqrt{3})^2/1,700$

$DB=1,275\ miles$

therefore

The shortest possible length for the bypass road is the distance DB (perpendicular distance from right angle to the hypotenuse triangle ABC)