GeometryIf the hypothenuse of right triangle of 26 cm long and one cathetus 14 cm longer than the other , find the lengths of the legs of triangle.
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
It is given that the hypotenuse of a right triangle is 26 cm long and one leg is 14 cm longer than the other.
Let the length of the shorter leg be x , the other leg is x + 14
AS it is a right triangle use hypotenuse theorem to write
x^2 + (x + 14)^2 = 26^2
=> x^2 + x^2 + 14^2 + 28x = 26^2
=> 2x^2 + 28x + 14^2 - 26^2 = 0
=> x^2 + 14x -240 = 0
=> x^2 + 24x - 10x - 240 = 0
=> x(x + 24) - 10(x + 24) = 0
=> (x - 10)(x + 24) = 0
We only take x = 10 as length cannot be negative
The lengths of the legs of the triangle are 10 and 24.
giorgiana1976 | College Teacher | (Level 3) Valedictorian
We'll note:
x = shorter leg
y = longer leg
z = hypothenuse
We'll apply Pythagorean Theorem in the given right triangle:
z^2 = x^2 + y^2
But y is 14 cm longer than x.
y = x + 14
We'll re-write Pythagorean Theorem:
z^2 = x^2 + ( x + 14)^2
But z = 26. We'll substitute z in the Pythagorean identity and we'll expand the square:
26^2 = x^2 + x^2 + 28x+ 196
We'll combine like terms:
676 = 2x^2 + 28x + 196
We'll divide by 2:
x^2 + 14a + 98 - 338 = 0
We'll combine like terms:
a^2 + 14x- 240 = 0
We'll apply quadratic formula:
x1 = [-14+sqrt(196 + 960)]/2
x1 = (-14+34)/2
x1 = 10
x2 = (-14-34)/2
x2 = -24
Since we are talking about a distance, which is always positive, we'll reject x2 = -24.
One cathetus of triangle is x = 10 cm and the other leg, y = 14 + 10 cm.
y = 24 cm