The perimeter of a right triangle is 24 cm. If its hypotenuse is 10 cm, find the other two sides. Find its area by using the formula area of a right triangle. Verify your result by using Heron’s formula
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ANSWER
Perimeter of the triangle =24 cm
AB+BC+AC=24
a+b+10=24
a+b=14 ............ (1)
From Pythagoras theorem,
AB
2
+BC
2
=AC
2
a
2
+b
2
=10
2
a
2
+b
2
=100 ........... (2)
Now,
(a+b)
2
=a
2
+b
2
+2ab
From (1) and (2),
(14)
2
=100+2ab
⇒2ab=196−100
2ab=96
ab=48
Area of the triangle =
2
1
×base×height
=
2
1
ab
=
2
48
=24 cm
2
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