3)The sides of ∆ABC are 10,10 and 5.
4)The lengths of sides of ∆XYZ are 29,29 and 48.
How to determine length of sides of issoceles triangle
3) ∆ABC is an isosceles triangle with base AB.
angleA = angleB(base angles of issoceles triangle)
Therefore,
AC = BC (equal sides of an isosceles triangle)
Given that
BC = 10 and AC = 3x + 4
10 = 3x +4
3x = 10-4
3x = 6
x = 6/3
= 2
Length of AC
3(2) + 4
6 + 4 = 10
Length of AB = x + 3
AB = 2 + 3 = 5
The sides of ∆ABC are 10,10 and 5.
4) From ∆XYZ
XZ is the base
since angle X = angle Z
Therefore,
XY = ZY(equal sides of an isosceles triangle)
4x + 1 = 29
4x = 29-1
4x = 28
x = 28/4
x = 7
Substitute into the expressions for the lengths to determine their size.
XY = 4x + 1
= 4(7) + 1
= 28 + 1
= 29
XZ = 7x - 1
= 7(7) - 1
= 49 - 1
= 48
The lengths of sides of ∆XYZ are 29,29 and 48.