Question

Find the length of the shorter leg of a right triangle with the longer leg is 9 feet more than the shorter leg the hypotenuse is nine feet less than twice the shorter leg

Answer 1

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

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

substituting the given values we get

$(2x-9)^{2} = (x)^{2}+(x+9)^{2}$

By using Identity (A ± B)² = A² ± 2AB +B²  we get

$4x^{2} -36x+81=x^{2} +(x^{2} +18x+81)\\\\4x^{2} -2x^{2} -36x-18x=81-81\\\\2x^{2} -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet$

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