Given: Triangle ABC is similar to triangle DEF. Segment AR is a median in triangle ABC and segment DS is a median in triangle DEF.
AB = 2x + 5, DE = x + 7, AR = 24, DS = 18. What is the value of x?
2006-10-14 16:52:36 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
It helps to draw a picture!
since ABC ~ DEF then ARB ~ DSE. you can set up a proportion and solve for x
median1 / leg 1 = median 2 / leg 2
24 / (2x + 5) = 18 / (x + 7) (cross multiply)
24(x + 7) = 18 ( 2x+5) (distribute)
24x + 168 = 36x+90 (isolate x)
78 = 12x (divide)
x = 6.5
hope this helps!
2006-10-14 17:07:38 · answer #1 · answered by lobster17 2 · 0⤊ 0⤋
The medians have the same ratio to one another as the ratios between the similar triangles that they cut.
the ratio of DS/AR is 18/24 or 3/4.
So, the ratio of DE/AB is also 3/4
which means that (x+7)/(2x+5)=3/4
cross multiply and you get 4((x+7)=3(2x+15)
or 4x+28=6x+15
get all the xs on one side by subtracting 4x from both sides: 4x+28-4x=6x+15-4x
28 = 2x +15
get all the integers on the other side by subtracting 15 from both sides:
28-15=2x+15-15
13 =2x
Solve for x by dividing both sides by 2
13/2 =2x/2
6.5 =x
2006-10-15 00:19:58 · answer #2 · answered by luka d 5 · 0⤊ 0⤋
x=ibdork
2006-10-15 00:00:52 · answer #3 · answered by St N 7 · 0⤊ 1⤋
GOD DAMN IT PEOPLE < DO YOUR OWN HOMEWORK
2006-10-14 23:54:42 · answer #4 · answered by sulfur_and_mercury 1 · 0⤊ 1⤋