Find the area (in m
2
) of the rectangular field, one of whose sides is 35m and a diagonal is 37m.
- A450
- B1295
- C1225
- D420
Solution & Step-by-step Explanation
Let the sides of the rectangle be a and b, and the diagonal be d.
Given:
a=35m
d=37m
According to Pythagoras' theorem in a right-angled triangle formed by the sides and the diagonal:
a
2
+b
2
=d
2
35
2
+b
2
=37
2
1225+b
2
=1369
b
2
=1369−1225=144
b=
144
=12m
Now, the area of the rectangular field is:
Area=a×b=35×12=420m
2
Given:
a=35m
d=37m
According to Pythagoras' theorem in a right-angled triangle formed by the sides and the diagonal:
a
2
+b
2
=d
2
35
2
+b
2
=37
2
1225+b
2
=1369
b
2
=1369−1225=144
b=
144
=12m
Now, the area of the rectangular field is:
Area=a×b=35×12=420m
2