8
81. The sides of a right-angled triangle are in
the ratio x: (x - 1): (x – 18). What is the
perimeter of the triangle?
Answers
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The perimeter of triangle is 56 units.
Given - Ratio of sides of triangle
Find - Perimeter of triangle
Solution - As the length of Hypotenuse is largest, so, x will be the hypotenuse of right angled triangle. As per the Pythagoras theorem, finding the value of x.
Hypotenuse² = Base² + Perpendicular²
x² = (x - 1)² + (x - 18)²
x² = x² + 1 - 2x + x² + 324 - 2*18*x
x² = x² + 1 - 2x + x² + 324 - 36x
Cancelling x²
x² + 325 - 38x = 0
Solving the equation
x² - 38x + 325 = 0
x² - 25x + 13x + 325 = 0
x (x - 25) + 13 (x - 25) = 0
x = 25 and - 13.
Since Hypotenuse can not be negative, hence, it's value is 25.
Value of other two sides = (x - 1) and (x - 18)
Value of other two sides = (25 - 1) and (25 - 18)
Value of other two sides = 24 and 7
Perimeter = sum of all sides of triangle
Perimeter = 25 + 24 + 7
Perimeter = 56
Hence, perimeter of given triangle is 56 units.