Question

Perimeter of triangle is 50cm . One sode of it is 4cm longer than the smaller side and tge third side is 6cm less than twice the smaller side. Find the area.

Answer 1

Let the smaller side of the triangle be(a) x cm.
Second side(b) = (4+x)cm.
Third side(c) = (2x-6)cm.
Given,
Perimeter = 50cm.
Therefore,
$\: \: \: \: \: \: \: \: 50 = x +( 4 + x) + (2x - 6) \\ =>50 = x + 4 + x + 2x - 6 \\ = > 50 = 4x - 2 \\ = > 4x = 52 \\ = >x = 13cm.$



Using Heron's formula,
Area
$= \sqrt{s(s - a)(s - b)(s - c)} \\ where \: \: \: \: \: s = \frac{ a+ b+ c}{2} \\ = \sqrt{25(25 - 13)(25 - 17)(25 - 20)} \\ = \sqrt{25 \times 12 \times 8 \times 5} \\ = \sqrt{5 \times 5 \times 5 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 } \\ = 5 \times 2 \times 2 \times 2 \sqrt{5 \times 3} \\ = 40 \sqrt{15} {cm}^{2}.$




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