Respuesta :
Answer:
Length of Shorter leg = 27 feet
Length of Longer leg = 36 feet
Length of Hypotenuse = 45 feet
Step-by-step explanation:
Given:
Let,
Length of Shorter leg = x,
According to the given condition we have
∴ Length of Longer leg = x + 9 feet
∴ Length of Hypotenuse = 2x - 9 feet
To Find:
Length of Shorter leg = ?
Solution:
Now In Right Angle Triangle, By Pythagoras theorem we have
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
substituting the given values we get
[tex](2x-9)^{2} = (x)^{2}+(x+9)^{2}\\[/tex]
By using Identity (A ± B)² = A² ± 2AB +B² we get
[tex]4x^{2} -36x+81=x^{2} +(x^{2} +18x+81)\\\\4x^{2} -2x^{2} -36x-18x=81-81\\\\2x^{2} -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet[/tex]
Substituting x=27 we get
∴ Length of Longer leg = x + 9 =27 +9 = 36 feet
∴ Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet
