Question

The area of the Δ ABC is `10sqrt3` cm², angle B is 60° and its perimeter is 20 cm , then l(AC) = ______.

Options

• 5 cm

• 10 cm

• 7 cm

• 8 cm

Answer 1

The area of the Δ ABC is `10sqrt3` cm², angle B is 60° and its perimeter is 20 cm , then l(AC) = 7 cm.

Explanation:

We have,

Area of triangle ABC = 10`sqrt3 "cm"^2`

Perimeter of triangle ABC = 20 cm

∠B = 60°

Area of Δ ABC = `1/2` ac sin B

`10sqrt3 = 1/2 "ac" xx sin 60°`

`10sqrt3 = 1/2 "ac" xx sqrt3/2`

ac = 40

cos`"B"/2 = sqrt(("s"("s - b"))/"ac")`

cos 30° = `sqrt((10 (10 - "b"))/40)  ...[because "s" = ("a + b + c")/2 = 20/2 = 10]`

`=> sqrt3/2 = sqrt(10 - "b")/2`

⇒ 3 = (10 - b)

⇒ b = 10 - 3 = 7 cm