Question

I need help with these two questions!! :)

Answer 1

1. Option B.

2. Option D.

Explanation:

1.

In the provided image, the straight line drawn in the triangle, divide the whole triangle into two triangles having a same angle with the corresponding sides proportional to each other. The area of these triangles is proportional to each other.

With the corresponding proportional sides,
`(x)/(6) = (5)/(8)`. x =
`(15)/(4)`.

2.

In the given image, ΔDEG ≅ ΔGEF.

Hence,
`(DE)/(DG) = (EF)/(FG) \\(8)/(X) = (12)/(14 - X) \\(2)/(X) = (3)/(14 - X) \\28 - 2X = 3X\\5X = 28\\X = 5.6`.