Trigonometry & Inverse Trigonometry
Properties Of Triangles
nta_abhyas_2025
Grade 11
Question:
If $a = 2$, then obviously $c = a - 1$, and then, from Eq. (i), $(a + 2)^2 = a(2a + 1)$. Find the value of $a$.
Step-by-Step Solution
Key Concept: Heron's formula is used to compute the area of a triangle given its three sides using the semi-perimeter.
The semi-perimeter is $s = \frac{2b + 2b + 30}{2} = 42$. Using Heron's formula with $s - a = \sqrt{(s-a)(s-b)(s-c)} = \sqrt{42(42-30)(42-30)(42-30)} = \sqrt{42 \cdot 12 \cdot 12 \cdot 12}$. Simplifying: $\sqrt{42 \cdot 16 \cdot 14 \cdot 12} = \sqrt{7 × 6 × 4 × 2} × \sqrt{(7-2)×(6-3)}$. The area equals $\frac{7 × 6 × 4 × 2}{42} = 8$.
Correct Answer: 4