SOLUTION: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x.
Algebra.Com
Question 658610: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x.
------
Use Pythagoras:
2(x+1)^2 = (x+5)^2
----
2[x^2 + 2x + 1] = x^2 + 10x + 25
---
2x^2 + 4x + 2 = x^2 + 10x + 25
x^2 -6x -23 = 0
---
x = [6 +- sqrt(36 - 4*-23)]/2
----
x = [6 +- sqrt(128)]/2
x = [6 +- 8sqrt(2)]/2
--
Positive solution:
x = 3 + 4sqrt(2)
===================
Cheers,
Stan H.
RELATED QUESTIONS
An isosceles right triangle has legs measuring (x-2) cm each. the hypotenuse has measure... (answered by stanbon)
An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has... (answered by stanbon)
an isosceles right-angled triangle has one side length of (x+2) cm and the length of the... (answered by Theo)
an isosceles right angled triangle has one side length of (x+2) cm and the length of the... (answered by KMST)
A right, isosceles triangle has hypotenuse length 50 cm. How long are the two... (answered by MathLover1,Alan3354)
What is the hypotenuse of a right triangle that has legs measuring 6 cm and 8... (answered by chessace)
In an isosceles right triangle, one of the congruent sides has a measure 7 cm. Find the... (answered by ewatrrr)
An isosceles triangle has a base of 30 cm and legs 17 cm each. What is the measure of a... (answered by Edwin McCravy)
An isosceles triangle has a base of 20 cm and legs measuring 36 cm. How long are the legs (answered by Earlsdon)