Question

In a triangle, if the longest side has length 15 cm, one of the another side has length 12 cm and its perimeter is 34 cm, then the area of the triangle in cm2 is:

• A. $$10 \sqrt{17}$$
• B. $$5 \sqrt{17}$$
• C. $$5 \sqrt{15}$$
• D. $10 \sqrt{15}$

Answer 1

Answer:

$$10 \sqrt{17}$$

Solution:

Given Data:

Side a (longest side) = 15 cm

Side b = 12 cm

Perimeter of triangle = 34 cm

Concept:

Perimeter of triangle = a + b + c and

Heron's formula for the area of triangle $=\rm\sqrt{[s(s - a)(s - b)(s - c)]}$

where s is the semi-perimeter.

Calculation:

Side c = Perimeter - a - b

⇒ 34 - 15 - 12 = 7 cm

Semi-perimeter (s) = Perimeter / 2 = 34 / 2 = 17 cm

Area $=\sqrt{[17(17 - 15)(17 - 12)(17 - 7)]}$

⇒ Area$=10\sqrt{17} cm^2$

Hence, the area of the triangle is approximately $10\sqrt{17} cm^2$