Question

the hypotenuse of a right triangle has a length of 14 units and side that is 9 units long. which equation can be used to find the length of the reaming side?

Answer 1

`\large\bf{\underline{\underline{\mathfrak{Question}:}}}`

The hypotenuse of a right triangle has a length of 14 units and side that is 9 units long. which equation can be used to find the length of the remaining side?

`\large\bf{\underline{\underline{\mathfrak{Solution}:}}}`

To solve the problems of a right angle triangle we commonly used Pythagoras theorem. It is the most widely used theorem which helps in finding the missing length of a right angle triangle.

According to Pythagoras theorem, the sum of square of base and the square of perpendicular give us square of hypotenuse.

`:{\Longrightarrow{\large{\rm{H^2=P^2+B^2}}}}`

In a right angle triangle there are two legs and a hypotenuse.

Given that,

`{:\Longrightarrow{\small{\rm{Hypotenuse\:of\:a\:right\:triangle=14\:units.}}}}`

`:{\Longrightarrow{\small{\rm{A\:side\:of\:a\:right\:triangle=9\:units.}}}}`

By putting these values in the Pythagoras theorem we get;

`:{\Longrightarrow{\small{\rm{14^2=9^2+B^2}}}}`

Let B = x

`:{\Longrightarrow{\small{\rm{196=81+x^2}}}}`

`:{\Longrightarrow{\small{\rm{196-81=x^2}}}}`

`:{\Longrightarrow{\small{\rm{115=x^2}}}}`

`:{\Longrightarrow{\small{\rm{√(115)=x}}}}`

Answer 2

According to Pythagorean theorem:

• c² = a² + b², where a and b legs and c- hypotenuse

To find the missing length of the leg we'll convert the equation:

• 14² = 9² + x²

Simplify:

• 196 = 81 + x²
• x² = 196 - 81
• x² = 115
• x = √115