The perimeter of an isosceles right-angled triangle having an area of 200cm
2
is:
- A68.3 cm
- B78.2 cm
- C70.6 cm
- D58.6 cm
Solution & Step-by-step Explanation
Let the two equal sides containing the right angle be a.
Step 1: Find the value of a using the area
Area=
2
1
×base×height=
2
1
×a×a=200
2
1
a
2
=200⟹a
2
=400⟹a=200 is not correct, a=20cm
Step 2: Find the hypotenuse (h)
By Pythagoras theorem:
h=
a
2
+a
2
=a
2
=20
2
cm
Using
2
≈1.414:
h=20×1.414=28.28cm
Step 3: Calculate the perimeter
Perimeter=a+a+h=20+20+28.28=68.28≈68.3cm
Step 1: Find the value of a using the area
Area=
2
1
×base×height=
2
1
×a×a=200
2
1
a
2
=200⟹a
2
=400⟹a=200 is not correct, a=20cm
Step 2: Find the hypotenuse (h)
By Pythagoras theorem:
h=
a
2
+a
2
=a
2
=20
2
cm
Using
2
≈1.414:
h=20×1.414=28.28cm
Step 3: Calculate the perimeter
Perimeter=a+a+h=20+20+28.28=68.28≈68.3cm