It is given that the area of triangle ABC is 35, and in the diagram, you’re given a height for triangle ABC. If you use BC as the base of the triangle, the triangle’s height is 7, so you can find the length of BC. The length BC, which is the base of triangle ABC, is also the hypotenuse of right triangle BDC. Given the hypotenuse and the length of leg BD, which is given in the diagram as 6, you’ll be able to find the third leg of the triangle, side DC, which is what you’re looking for.
Going back to triangle ABC, the area is 35 and the height is 7. The area of a triangle is
x base x height.
So,
x base x height is 35. Therefore,
x 7 x length
BC is 35. That means 7 × length BC is 70, so BC must have length 10. Now look at right triangle BDC. Here is a right triangle with one leg of length 6, the hypotenuse of length 10, and the third side unknown. That’s one of the famous Pythagorean ratios—it’s a 3:4:5 triangle. So DC must have length 2 × 4, or 8.