the length of the sides forming right angle of a right angled triangle are 5x and (3x-1) cm. If the area of the triangle 60 cm².Find it'shypotenius .
Answers
Answer:
1/2 bh
1/2 (5x (3x-1)) = 60
1/2 (15x^2 -5x ) = 60
15x^2 - 5x = 120
15x^2 -5x - 120 = 0
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 = -8/3
since length cannot be -ve
x = 3
so the sides of the triangle are
5(3) and 3(3) - 1
15 and 8
Pythogorean prop
8^2 + 15^2 = hypotenuse ^2
(sum of the squares on the two non - hypotenuse sides is equal to the square on the hypotenuse )
64 + 225 = 289
hypotenuse sqr = 289
hy[otenuse = Route of 289
Hyp - 17 !
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Given:
height =5x cm
base=(3x-1) cm
Area of a triangle=60 cm²
Solution:
Area of a triangle=(1/2)×base× height
60=1/2×5x×(3x-1)
5x(3x-1)=60×2
5x(3x-1)=120
x(3x-1)=120/5
3x²-x=24
3x²-x-24=0
3x²+8x-9x-24=0
x(3x+8)-3(3x+8)
(x-3)(3x+8)
x=3 (or) x=-3/8.
This gives x=3
Since length can't be in negative, so we choose the value as x=3.
Thus, height =4x= 4×3 =12 cm
Breadth = (2x-1) = 2×3-1=5 cm
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
h² = 15²+ 8²
= 225 + 64
= 289
h =√289
=17.
Therefore the hypotenuse = 17cm.
Therefore the sides of the triangle are 8cm,15cm, and 17cm.