Answer:
a = 8
b = 17
Step-by-step explanation:
We are given the following:
An isosceles triangle with perimeter [tex]20x + 35[/tex].
Property of Isosceles Triangle:
- Two sides out of three sides of an isosceles triangle are equal.
Thus, the two equal sides of the triangle from given daigram is:
[tex]ax+9[/tex]
The third side is :
[tex]4x + b[/tex]
Perimeter of triangle =
[tex]\text{Sde 1 + Side 2 + Side 3}[/tex]
Putting the values, we have:
[tex]20x + 35 = 2(ax+9) + (4x + b)\\20x + 35 = 2ax + 18 + 4x + b\\20x + 35 = (2a+4)x + (18+b)\\\text{Comparing both sides of the equation}\\2a + 4 = 20\\\Rightarrow 2a = 20-4 = 16\\a = 8\\18+b = 35\\\Rightarrow b = 35-18 = 17[/tex]
Thus value of a is 8 and b is 17.
