Question

The area of triangle with given two sides 18cm and 10cm, respectively and perimeter equal to 42 cm is:

• A. 20$\sqrt{11}c{m}^2$
• B. 19$\sqrt{11}c{m}^2$
• C. 22$\sqrt{11}c{m}^2$
• D. 21$\sqrt{11}c{m}^2$

Answer 1

The correct option is D 21$\sqrt{11}c{m}^2$

Explanation : Perimeter = 42
a + b + c = 42
18 + 10 + c = 42
c = 42 - 28 = 14 cm
Semi perimeter, s = $\frac{42}{2}=21cm$
Using Heron's formula :
$A=\sqrt{s(s-a)(s-b)(s-c)}A=\sqrt{21(21-18)(21-10)(21-14)}A=\sqrt{21\times 3\times 11\times 7}=\sqrt{7\times 3\times 3\times 11\times 7}=21\sqrt{11}$
Put the values of s, a, b and c, to get the answer equal to 21$\sqrt{11}c{m}^2$.