Find the area, to the nearest cm2, of the triangle whose sides are in the ratio 2 : 3 : 4 and whose perimeter is 180 cm.
A.
1162 cm2
B.
1163 cm2
C.
1160 cm2
D.
1161 cm2
Correct Answer: 1162 cm2
Explanation
Let the length of the sides of triangle be 2x, 3x and 4x.
Perimeter of triangle = 180cm
⇒ 2x + 3x + 4x = 180
⇒ 9x = 180
⇒ x=180/9
= 20 cm
Then the sides of the triangle are:
2x = 2 × 20 = 40 cm; 3x = 3 × 20 = 60cm and 4x = 4 × 20 = 80cm
Using Heron's formula
Area of triangle = s√(s−a)(s−b)(s−c)
Where s = (a + b + c)/2
Let a = 40cm, b = 60cm, c = 80cm and s = (40 + 60 + 80)/2 =180/2 = 90cm
⇒ A = √90(90−40)(90−60)(90−80)=√90×50×30×10=√(1350000)
∴ A =1162cm2 (to the nearest cm2)
Let the length of the sides of triangle be 2x, 3x and 4x.
Perimeter of triangle = 180cm
⇒ 2x + 3x + 4x = 180
⇒ 9x = 180
⇒ x=180/9
= 20 cm
Then the sides of the triangle are:
2x = 2 × 20 = 40 cm; 3x = 3 × 20 = 60cm and 4x = 4 × 20 = 80cm
Using Heron's formula
Area of triangle = s√(s−a)(s−b)(s−c)
Where s = (a + b + c)/2
Let a = 40cm, b = 60cm, c = 80cm and s = (40 + 60 + 80)/2 =180/2 = 90cm
⇒ A = √90(90−40)(90−60)(90−80)=√90×50×30×10=√(1350000)
∴ A =1162cm2 (to the nearest cm2)
