Answer :
Answer:
[tex]Perimeter=(10+4\sqrt{10}) inches[/tex]
Step-by-step explanation:
Let the length of one leg of the right angle triangle=x
The length of the other leg is three times as large as the length of the other leg = 3x
The Length of the hypotenuse=10 inches
From Pythagoras theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
[tex]10^2=x^2+(3x)^2\\100=x^2+9x^2\\100=10x^2\\x^2=100/10=10\\x=\sqrt{10}[/tex]
The Lengths of the triangle are therefore: [tex]\sqrt{10} ,3\sqrt{10} and 10 inches[/tex]
Perimeter=Sum of all the lengths
[tex]=\sqrt{10} +3\sqrt{10} + 10 inches\\=(10+4\sqrt{10}) inches[/tex]
Answer:
Perimeter == 10 + 4√10
Step-by-step explanation:
Let the length of the smaller leg be x and thus since the bigger leg is 3 times the size of the smaller one, the bigger leg is 3x.
Now, from the question we are given that the hypotenuse is 10 inches.
Now since this is a right angle triangle, let's use Pythagoras theorem to which says;
a² + b² = c²
Where c is the hypotenuse, while a and b are the other sides of the triangle.
Thus, fixing x and 3x for a and b respectively and 10 for c, we have;
x² + (3x)² = 10²
So, x² + 9x² = 100
Thus, 10x² = 100
Divide both sides by 10 to get,
x² = 10
Take square root of both sides to get ; x = √10
Thus since one side is x and the other 3x,thus the dimensions of the triangle are √10, 3√10 and 10.
Now, perimeter of triangle is the sum of all 3 sides.
Thus perimeter = (√10) + 3(√10) + 10
= 10 + 4√10