Question

What is the area of an isosceles triangle whose tow sides are 12 cm and one side is 16 cm

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

32√5 cm².

Step-by-step explanation:

$\text{Given two equal sides of triangle, 12 cm each and an unequal side = 16 cm.}\\\\\text{Thus, area of triangle = } \sqrt{s((s-a)(s-b)(s-c)},\\\\\text{Where, a, b and c are the three sides of the triangle. Here, since it is an isosceles triangle, a =b}\\\\\text{And, s is the semiperimeter = } \dfrac{a+b+c}{2} \: \: or \: \dfrac{2a + c}{2} \: \text{in this case.}\\\\\text{Thus, area = } \sqrt{s(s-a)(s-a)(s-c)}\\\\\text{a = 12 cm; b = 16 cm; s = } \dfrac{2(12) + 16}{2} = \dfrac{24+16}{2}$

$\implies s = \dfrac{40}{2} = 20 \: cm\\\\\\\text{Now, finally, area of triangle}\\\\= \sqrt{s(s-a)(s-a)(s-c)}\\\\= \sqrt{20(20-12)(20-12)(20-16)}\\\\= \sqrt{20 \times 8 \times 8 \times 4}\\\\= \sqrt{2 \times 2 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}\\\\= \sqrt{2^{10} \times 5}\\\\= \sqrt{(2^5)^{2} \times 5}\\\\= 2^5 \sqrt{5}\\\\= \boxed{32 \sqrt{5} \: cm^2}$

Hope it helps.