Solution:
Given:
In an isosceles triangle,
Length of base (b) = 10m
Area (A) = 60 sq m
To find:
Length of each equal sides (a)
By formula,
Area of an isosceles triangle (A) = \(\frac b4\sqrt{4a^2-b^2}\)
Or, 60m2 = \(\frac{10}4\sqrt{4a^2-10^2}\)
Or, \(\frac{4\times60}{10}=\sqrt{4a^2-100}\)
Or, \(24=\sqrt{4a^2-100}\)
Squaring both sides we get,
\(\left(24\right)^2=\left(\sqrt{4a^2-100}\right)^2\)
Or, \(576=4a^2-100\)
Or, \(4a^2=676\)
Or, \(\frac{676}4=a^2\)
∴ a = 13 m
Hence, the measure of remaining equal sides of the triangular piece of the land is 13m.... is the required answer
