Hypotenuse of a right-angled triangle is 41 cm. If one of the remaining 2 sides is 9cm, find the length of other side.
Answers
Answered by
1
Answer:
Area =180cm
2
2
ab
=180
ab=2×180=360
Applying Pythagoras theorem on right triangle shown above;
a
2
+b
2
=41
2
a
2
+b
2
=1681
a
2
+b
2
−2ab=1681−2ab
(a−b)
2
=1681−2(360)=1681−720=961
a−b=
961
=31 cm
The difference between the lengths of the legs of the triangles must be 31 cm.
Answered by
1
Consider the above figure,
Given,
AC=41 cm and Area of △ABC=180 cm
2
We know that, by Pythagoras theorem
AB
2
+BC
2
=AC
2
AB
2
+BC
2
=41
2
...... (i)
Area of ABC=
2
1
×BC×AB
BC×AB=180×2=360 ...... (ii)
We have,
(AB−BC)
2
=AB
2
+BC
2
−2×AB×BC
Substitute from (i) and (ii) here,
(AB−BC)
2
=41
2
−2×360=1681−720=961
(AB−BC)=31 cm
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