the perimeter of a right angle triangle is 30cm and hypotenuse is 13cm .Find the Length of other 2 sides of the triangle
Answers
Answer:
answer 17 of l lengths
Step-by-step explanation:
answer 17 of length
With the perimeter being 30 cm, we know the length of all 3 sides.
x + y + z = 30
The known hypotenuse is 13 cm, so I'll call that "z":
x + y + 13 = 30
x + y = 17
now we can set up Pythagorean Theorem in terms of "x" and "y", then we'll have a second equation to make a system of equations to solve:
a² + b² = c²
x² + y² = 13²
x² + y² = 169
Substitute the expression for y in terms of x, then we can solve for x:
y = 17 - x
x² + y² = 169
x² + (17 - x)² = 169
x² + 289 - 34x + x² = 169
2x² - 34x + 120 = 0
Divide both sides by 2:
x² - 17x + 60 = 0
factor:
(x - 5)(x - 12) = 0
x = 5 and 12
Now that we have two x's, we can solve for the two y's:
y = 17 - x
y = 17 - 5 and y = 17 - 12
y = 12 and y = 5
the other two lengths are :12 cm and 5 cm.