A semicircle is drawn over a diameter. The circum- ference of the semicircle is 72 units. I(BC) =/(AO)=(OC). Find the perimeter of A ABC.
Answers
Answer:
Perimeter of Δ ABC = 109 units
Step-by-step explanation:
Given:
Circumference of semi-circle = 72 units
l(BC) = l(AO) = l(OC)
We need to find the perimeter of the Δ ABC.
Perimeter of a Δ = Sum of all three sides = AB + BC + AC
For that we first have to find the radius of circle i.e. OC
Circumference of a semi-circle = πr
72 = 22/7 × r
72 × 7 / 22 = r
∴ r = 22.9 ≈ 23 units
So, OC = OA = 23 units
As, BC = OA
So, BC = 23 units
AC = OA + OC
= 23 + 23
∴ AC = 46 units
Now, we have to find l(AB)
∠ABC = 90° (Given)
Apply pythagoras theorem on Δ ABC,
Hypotenuse² = Base² + Perpendicular²
AC² = AB² + BC²
(46)² = AB² + (23)²
AB² = (46)² - (23)²
AB² = (46+23) (46-23) {Using identity a² - b² = (a+b) (a-b)}
AB² = 69 × 23
AB² = 1587
AB = √1587
AB = 39.8 ≈ 40 units
Perimeter of Δ ABC = AB + BC + AC
= 40 + 23 + 46 = 109 units
Answer:
taking side AC of triangle ABC as diameter or semi circle is drawn the circumference of the semicircle is 72 units length BC is equals to length AO is equal student OC find the perimeter of triangle ABC