the radius of the circle whose area is the sum of the area of two triangles whose sides are 35, 53, 66 and 33, 56, 65, measure in centimetres, will be:
1) 4.62 cn
2) 9.24cm
3)14 root 3 cm
4)11.24 cm
Answers
Answer:
R = 14√3 cm
option 3
Step-by-step explanation:
The radius of the circle whose area is the sum of the area of two triangles whose sides are 35, 53, 66 and 33, 56, 65,
Area of triangle with sides 35 . 53 & 66 cm
s = (35 + 53 + 66)/2 = 77
Area of triangle using hero formula
= √s(s-a)(s-b)(s-c)
=√77(77-35)(77-53)(77-66)
=√77 * 42 * 24 * 11
=√(7 * 11) ( 2 * 3 * 7) *( 2 * 2 * 2 *3) *( 11 )
= 2 * 2 * 3 * 7 * 11
= 924 cm²
Similarly
Area of triangle with sides 33 . 56 & 65 cm
s = (33 + 56 + 65)/2 = 77
Area of triangle using hero formula
= √s(s-a)(s-b)(s-c)
=√77(77-33)(77-56)(77-65)
=√77 * 44 * 21 * 12
=√(7 * 11) ( 2 * 2 * 11) *( 3 *7) *( 2 * 2 * 3)
= 2 * 2 * 3 * 7 *11
== 924 cm²
Total Area = 924 + 924 = 1848 cm²
Area of circle = π R²
(22/7) R² = 1848
=> R² = 84 * 7
=> R² = 2 * 2 * 3 * 7 * 7
=> R = 14√3 cm
option 3
Answer: Option (3)
14
Step-by-step explanation:
The radius of the circle whose area is the sum of the area of two triangles whose sides are 35, 53, 66 and 33, 56, 65.
Area of triangle with sides 35,53 & 66 cm
s = (35 + 53 + 66)/2 = 77
Area of triangle using Heron's formula
= √s(s-a)(s-b)(s-c)
=√77(77-35)(77-53)(77-66)
=√77 * 42 * 24 * 11
=√(7 * 11) ( 2 * 3 * 7) *( 2 * 2 * 2 *3) *( 11 )
= 2 * 2 * 3 * 7 * 11
= 924 cm²
Similarly,
Area of triangle with sides 33,56 & 65 cm
s = (33 + 56 + 65)/2 = 77
Area of triangle using Heron's formula
= √s(s-a)(s-b)(s-c)
=√77(77-33)(77-56)(77-65)
=√77 * 44 * 21 * 12
=√(7 * 11) ( 2 * 2 * 11) *( 3 *7) *( 2 * 2 * 3)
= 2 * 2 * 3 * 7 *11
= 924 cm²
Total Area = 924 + 924 = 1848 cm²
Area of circle = π R²
(22/7) R² = 1848
=> R² = 84 * 7
=> R² = 2 * 2 * 3 * 7 * 7
=> R = 14√3 cm