The hypotenuse of a right triangle is 3 root 10 cm.If the smaller leg is tripled and longer leg is doubled,the new hypotenuse will be 9 root 5 cm.Is it possible to draw such a right triangle ?If so,how long are they?
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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