1. If triangles EIO = UAN, EI = 3x-4, IO = 2x+5, UA = 2x+3 and UN = 3x+1, solve for the value of x, find the perimeter of triangle UAN and identify the smallest angle in triangle EIO.
2. If triangle FAT is equal to triangle GRC, FA = 24cm and the ratio of GR, RC and GC is 2:1:3, respectively, find the perimeter of triangle FAT, GC and AT.
since the triangle are congruent, we know that
EI=UA, so 3x-4 = 2x+3; x=7
Now you can find all the sides, and so on.
For the other, you have
FA = GR = 24
So,
GR:RC:GC = 2:1:3 = 24:12:36
and now you can go on.
1. To solve for the value of x and find the perimeter of triangle UAN, we can start by setting up and solving an equation based on the given information.
Since triangles EIO = UAN, their corresponding sides must be equal.
We have:
EI = 3x - 4
IO = 2x + 5
UA = 2x + 3
UN = 3x + 1
Setting the corresponding sides equal to each other, we get:
3x - 4 = 2x + 3
3x - 2x = 3 + 4
x = 7
Now that we have found the value of x, we can substitute it back into the expressions to find the lengths of the sides:
EI = 3x - 4 = 3(7) - 4 = 21 - 4 = 17
IO = 2x + 5 = 2(7) + 5 = 14 + 5 = 19
UA = 2x + 3 = 2(7) + 3 = 14 + 3 = 17
UN = 3x + 1 = 3(7) + 1 = 21 + 1 = 22
To find the perimeter of triangle UAN, we add up the lengths of its three sides:
Perimeter = UA + UN + AN
= 17 + 22 + 17
= 56
To identify the smallest angle in triangle EIO, we need additional information like the measure of one of the angles.