. The sides of a right-angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the
length of the hypotenuse of the triangle if its area is 60 \mathrm{cm}^{2}
Consider ABC as a right-angled triangle
AB = 5x cm and BC = (3x – 1) cm
We know that
Area of △ABC = ½ × AB × BC
Substituting the values
60 = ½ × 5x (3x – 1)
By further calculation
120 = 5x (3x – 1)
Taking out the common terms
3x (x – 3) + 8 (x – 3) = 0
(3x + 8) (x – 3) = 0
Here
3x + 8 = 0 or x – 3 = 0
We can write it as
3x = -8 or x = 3
x = -8/3 or x = 3
x = -8/3 is not possible
So x = 3
AB = 5 × 3 = 15 cm
BC = (3 × 3 – 1) = 9 – 1 = 8 cm
In right-angled △ABC
Using Pythagoras theorem
Therefore, the hypotenuse of the right angled triangle is 17 cm.
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