in rst, if s=t, rs=9x-13, st=10x-3, and rt=4x+2, find x and the measurement of each side

Question

1. in rst, if s=t, rs=9x-13, st=10x-3, and rt=4x+2, find x and the measurement of each side

x=

rt=

st=

In acd, if ac=cd, a=3x-4, c=5x+1, and d=7x-27, find x and the measure of each angle

x=

a=

c=

d=

Answer 1

(1) Since s=t, rs=rt.

So rs = 9x - 13 = rt = 4x + 2.

Since 9x - 13 = 4x + 2,

9x - 4x = 2 + 13

So 5x = 15, and x=3.

Since x=3, rs = 9x - 13 = 9(3) - 13 = 27 - 13 = 14, and st = 10x - 3 = 10(3) - 3 = 30 - 3 = 27 and rt = 4x + 2 = 4(3) + 2 = 12 + 2 = 14.

So x=3, rs=14, st=27 and rt=14.

(2) Since ac=cd, a = d.

So a = 3x - 4 = d = 7x - 27.

Then 3x - 4 = 7x - 27

So -4 + 27 = 7x - 3x

And 23 = 4x, so x = 23/4.

Since x=23/4,

a = 3x - 4 = 3(23/4) - 4 = (69/4) - 4 = (69/4) - (16/4) = (69 - 16) / 4 = 53/4

c = 5x + 1 = 5(23/4) + 1 = (115/4) + 1 = (115/4) + (4/4) = 119/4

d = 7x - 27 = 7(23/4) - 27 = (161/4) - 27 = (161/4) - (108/4) = 53/4

So x=23/4, a=53/4, c=119/4 and d=53/4.

Answer 2

I assume we're talking about triangles? If so...

1. In rst: Since s=t, then rs=rt. Therefore, 9x-13=4x+2. Solve for x, then substitute to find rt & st.
2. In acd: Since ac=cd, then a=d. So you can use the same process as in #1 to solve for x and find the rest of what's being requested.