The right triangle
Geometry
Level
2
The length of one of the legs of a right angled triangle exceeds the length of the other leg by 10 cm but is smaller than that of the hypotenuse by 10 cm. Find the length of the hypotenuse.
The answer is 50.
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1 solution
Let,
Given side=x cm
Therefore,
.'.Hypo. = x+10 cm
.'.III Side = x-10 cm
Accor. to Pythagoras' Thm.,
Hypo^2 = Side I^2 = Side II^2
.'.(x+10)^2 = x^2 + (x-10)^2
.'.,As we Know;
x^2 + 20x + 100 = x^2 + x^2 - 20x + 100
.'. 0 = 2x^2 - x^2 - 20x - 20x +100 -100
.'. 0 = x^2 - 40x
.'. 40x = x^2
.'. 40x/x = x
.'. 40 = x
.'.x = 40 cm
.'.Hypo. = x + 10 cm
.'.Hypo. = 40 cm + 10 cm
.'.Hypo. = 50 cm