the difference in the sides along the right angle in a right traingle is 14 cm if the area of triangle is 120 c. find the perimeter of the triangle
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the difference in the sides along the right angle in a right traingle is 14 cm if the area of triangle is 120 c. find the perimeter of the triangle
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Answer:
Let the sides at right angles in the given right-angled triangle be a and b.
Without loss of generality, we let a>b.
The by the problem a−b=14⇒a=(b+14)........(1).
Now the are of the right-angled triangle be
2
1
×a×b=
2
b(b+14)
cm
2
. [Using (1)]
According to the problem
2
b(b+14)
=120
b
2
+14b−240=0
(b−10)(b+24)=0
This gives b=10⇒a=24.
Now the hypotenuse of the right-angled triangle be
10
2
+24
2
=26 cm.
Now the perimeter of the triangle be (10+24+26)=60 cm.