Question

if the area of isoceles triangle is 240cm sq and its base is 20 cm find the length of its equal side

Answer 1

Answer:

19.6cm

Step-by-step explanation:

By Heron's formula:

Area = $\sqrt{s(s-a)(s-b)(s-c)}$   (i)

where, s = $\frac{a+b+c}{2}$

but as it is isosceles Δ, a=b and c = 20cm

s = $\frac{2a+20}{2}$

using (i)

240 = $\sqrt{\frac{2a+20}{2}(\frac{2a+20}{2} - a) (\frac{2a+20}{2} - a)(\frac{2a+20}{2} - 20)}$

240 = $\sqrt{\frac{2a+20}{2}(10)(10)(2a-20) }$

240 = $\sqrt{50(2a+20)(2a-20)}$ (a+b)(a-b) = a²-b²

240 = $\sqrt{200a^{2} - 20000}$

$240^{2}$ = $200a^{2} -20000$

$200a^{2} = 77600$

    a² = $\frac{77600}{200}$

    a = $\sqrt{388}$ = 19.6

∴ each equal side is 19.6cm in length