Answer:
60 cm
Explanation:
This is a very complex question and took me time to get the 1st step done mentally but I got it :
Perimeter of a right angle triangle is given by the formula :
P = a+b + √(a²+b²)
We need the 2 shorter legs for this formula but we only have these expressions for b and c. So let's solve for a using pythagoras' theorem :
b = a+5
c = a+10
To solve for a, we use pythagoras :
a = √{c² - b²}
a = √{ (a²+20a+100) - (a²+10a+25) }
a = √(10a+75)
a² = 10a+75
a²-10a-75 = 0
Now we use the factorization method to solve for a :
(a-15)(a+5)=0
a= 15 , a=-5
We take the positive value as a cannot be a negative length.
Now we have the value of a of 15, we can use this for b and then put it into the perimeter formula :
b = a+5
b = 15 + 5
b = 20
Now we substitute a and b into the perimeter formula :
P = a+b + √(a²+b²)
P = 15 + 20 + √(15²+20²)
P = 35 + √(225+400)
P = 35 + √625
P = 35 + 25 = 60
Units will be cm
So our final answer is a perimeter of 60 cm
Hope this helped and have a good day