Question 12 Marks
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Answer
a = 12 cm, b = 12 cm
Perimeter = 30 cm
a + b + c = 30
⇒ 12 + 12 + c = 30
⇒ 24 + c = 30
⇒ c = 30 – 24
⇒ c = 6 cm
s = $\frac{30}{2}$ cm = 15 cm
∴ Area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{15(15-12)(15-12)(15-6)}$
$=\sqrt{15(3)(3)(9)}=9\sqrt{15}$ cm2
View full question & answer→a = 12 cm, b = 12 cm
Perimeter = 30 cm
a + b + c = 30
⇒ 12 + 12 + c = 30
⇒ 24 + c = 30
⇒ c = 30 – 24
⇒ c = 6 cm
s = $\frac{30}{2}$ cm = 15 cm
∴ Area of the triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{15(15-12)(15-12)(15-6)}$
$=\sqrt{15(3)(3)(9)}=9\sqrt{15}$ cm2