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

13√2

Step-by-step 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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)