THE HYPOTENUSE OF A RIGHT TRIANGLE IS 3(root)10 CM. IF THE SMALLER LEG IS TRIPLED AND THE LONGER LEG IS DOUBLED,NEW HYPOTENUSE WILL BE 9(root)5 CM.HOW LONG ARE THE LEGS OF THE TRIANGLE? (3 MARKS)
Answers
SOLUTION :
Given : Hypotenuse of a right triangle is 3√10 cm.
Let the length of smaller leg be x cm and the larger leg be y cm.
By using Pythagoras theorem,
H² = B² + P²
x² + y² = (3√10)²
x² + y² = 9×10
x² + y² = 90
y² = 90 - x² . ………….(1)
Given if the smaller leg is tripled and the longer leg is doubled, new hypotenuse will be 9√5 cm
Smaller leg = 3x
longer leg = 2y
By using Pythagoras theorem,
H² = B² + P²
(3x)² + (2y)² = (9√5)²
9x² + 4y² = 81×5
9x² + 4y² = 405
9x² + 4(90 - x²) = 405
[From eq 1]
9x² + 360 - 4x² = 405
9x² - 4x² + 360 - 405 = 0
5x² - 45 = 0
5x² = 45
x² = 45/5
x² = 9
x = √9
x = ±3
Since, length of a side can't be negative, so x ≠ - 3
Therefore, x = 3
Length of smaller leg be 3 cm
On putting x = 3 in eq 1,
y² = 90 - x²
y² = 90 - 3²
y² = 90 - 9
y² = 81
y = √81
y = ± 9
Since, length of a side can't be negative, so y ≠ - 9
Therefore, y = 9
Length of larger leg be 9 cm
Hence, the length of smaller leg be 3 cm and the larger leg be 9 cm.
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