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a right triangle with one leg 5 cm longer than the other and the hypotenuse 10 cm longer than the shorter leg. What is the perimeter of the​ triangle?

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9 votes

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

User Burton Kent
by
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