6: The perimeter of a right-angled triangle is 12 cm and its area is 6 cm. Find the sides of the triangle.
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2
Answer:
a+b+5=12
a+b=7⇒a=7−b...(1)
a
2
+b
2
=5
2
a
2
+b
2
=25...(2)
From (1) and (2)
(7−b)
2
+b
2
=25
49+b
2
−14b+b
2
=25
2b
2
−14b+24=0
b
2
−7b+12=0
(b−4)(b−3)=0
⇒b=4,3
a=7−b⇒a=3,4
Area=
2
1
×4×3=6sq. units
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