Question

The length of a side of a triangle is 26 in. A line, parallel to the given side ,divides the triangle into 2 parts of equal areas. Find the length of the segment cut from the line by the two other sides of the triangle

Answer 1

13√2

Explanation:

The areas of the larger triangle, and the smaller triangle (formed when the larger triangle was cut by the parallel line) are similar. Therefore we can compare their areas:

Area1/Area2 = (Length1)^2/(Length2)^2,

x/2x = (Length1)^2/(26)^2,

1/2 = (Length1)^2/676,

(Length1)^2 = 676/2 = 338

Length1 = √1352 = 13√2