The perimeter of a right-angled triangle is 24 cm and its area is 24 cm Find the
sides of the triangle.
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Step-by-step explanation:
Perimeter of the triangle =24 cm
AB+BC+AC=24
a+b+10=24
a+b=14 ............ (1)
From Pythagoras theorem,
AB2+BC2=AC2
a2+b2=102
a2+b2=100 ........... (2)
Now,
(a+b)2=a2+b2+2ab
From (1) and (2),
(14)2=100+2ab
⇒2ab=196−100
2ab=96
ab=48
Area of the triangle =21×base×height
=21ab
=248
=24 cm2
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