Q91 of 134 Page 4


The hypotenuse of a right triangle is 3√10 cm. If the smaller legis tripled and the longer leg doubled, new hypotenuse will be
9√ 5 cm. How long are the legs of the triangle?


Hypotenuse = cm
Let the smaller leg be x cm


New Smaller leg = 3x cm

New Longer leg = cm

New hypotenuse = cm
81× 5 = 9x 2 + 4(90 – x 2 )
405 = 9x 2 + 360 – 4x 2
45 = 5x 2
x 2 – 9 = 0
(x – 3)(x + 3) = 0
(x – 3) = 0 or (x + 3) = 0
x = 3 or x = -3

Since x cannot be negative
The smaller leg is 3cm and the longer leg is

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