The sides of a right-angled traingle containing the right angle (5x) cm and (3x -1) cm If its area is 60 cm², find its perimeter.
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Answer:
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Step-by-step explanation:
Given that sides of a right-angled triangle are 5x and (3x - 1)cm.
Given that Area of the triangle = 60cm^2.
We know that Area of the triangle = 1/2 * b * h
60 = 1/2 * 5x * (3x - 1)
5x(3x - 1) = 60 * 2
5x(3x - 1) = 120
x(3x - 1) = 120/5
3x^2 - x = 24
3x^2 - x - 24 = 0
3x^2 + 8x - 9x - 24 = 0
x(3x + 8) - 3(3x + 8)
(x - 3)(3x + 8)
x = 3 (or) x = -3/8.
x value should not be -ve.Therefore the value of x = 3.
Therefore the sides of a right-angled triangle =
5x = 5 * 3 = 15cm
(3x - 1) = (3 * 3 - 1)
= 9 - 1
= 8cm
By Pythagoras theorem, we know that
h^2 = 15^2 + 8^2
= 225 + 64
= 289
h = \sqrt{289}
289
= 17.
Therefore the hypotenuse = 17cm.
Therefore the sides of the triangle are 8cm,15cm, and 17cm.
Hope this helps!
Answer:
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