Answer:
The length and base are 10/3 and 25/3 respectively
Step-by-step explanation:
Given:
Represent the sides with S and the base with B
Shape: Isosceles Triangle
[tex]S= B- 5[/tex]
[tex]Perimeter , P= 15[/tex]
Required
Determine the base and legs of the triangle;
The perimeter (P) of a triangle is calculated as thus;
[tex]P = S+ S + B[/tex]
[tex]P = 2S + B[/tex]
Substitute B- 5 for S
[tex]P = 2(B - 5) + B[/tex]
[tex]P = 2B - 10 +B[/tex]
Substitute 15 for P
[tex]15 = 2B - 10 + B[/tex]
Collect Like terms
[tex]2B + B = 15 + 10[/tex]
[tex]3B = 25[/tex]
Divide through by 3
[tex]B = \frac{25}{3}[/tex]
Recall that [tex]S= B- 5[/tex]
[tex]S = \frac{25}{3} - 5[/tex]
Take LCM
[tex]S = \frac{25 - 15}{3}[/tex]
[tex]S= \frac{10}{3}[/tex]
Hence, the length and base are 10/3 and 25/3 respectively
