Given: ΔABC, AB = BC
Perimeter of ΔABC = 50
Perimeter of ΔABD = 40
Find: BD
BD is the altitude and I got 15,
15+20+5=40
20+20+10=50
2x+y=50
x+1/2y+(a^2+b^2=c^2)
x=15
Interesting. I did it like this:
2x+2y = 50, so x+y=25
x+y+h = 40
25+h = 40
h = 15
works for me.
I hope you calculated BD and didn't just guess around till you got a number that worked.
15 units is correct.
no its units not inches
it doesnt matter anyway
Thx
To find the length of BD, we can use the given information about the perimeters of triangles ABC and ABD.
First, let's analyze triangle ABC. Since AB is equal to BC (given), we can divide the perimeter of triangle ABC (50) in two equal parts: 25 for each side (AB and BC).
Next, let's look at triangle ABD. We know that the perimeter of triangle ABD is 40. We can divide this perimeter in two parts: 20 for sides AB and BD each.
Now, we have the information we need to find the length of BD.
To calculate BD, we subtract the sum of the lengths of AB and BC from the perimeter of triangle ABD:
Perimeter of ABD = AB + BD + AD
40 = 20 + BD + AD
Since AD is a part of the perimeter of triangle ABC, we can subtract the length of AD from the 25 obtained earlier:
Perimeter of ABC = AB + BC + AC
50 = 25 + 25 + AC
AC = 50 - 50
AC = 25
Now, we can substitute the values of AB (20), AC (25), and the perimeter of ABD (40) into the equation for perimeter of ABD:
40 = 20 + BD + 25
By simplifying the equation, we can find the length of BD:
BD = 40 - 20 - 25
BD = 15
Therefore, the length of BD is 15.