the length of isoceles triangle is 10cm if its altitude is 1cm shorter than its equal sides find area of triangle
Given, the base of an isosceles triangle = BC = 10 cm
Let the equal sides AB and AC of isosceles triangle be x cm.
∴ AB = AC = x cm
Now, altitude of triangle AD = (x - 1) cm
We know that, in an isosceles triangle altitude from the opposite vertex will always bisect the base.
So, BD = DC =
Now, In Δ ABD by pythagoras theorem,
AB2 = AD2+ BD2
⇒ x2 = (x-1)2+ 52
⇒ x2 = x2+ 1 - 2x + 25
⇒ -26 = -2x
⇒ x = 13 cm
So, AD = x - 1 = 13 - 1 = 12 cm
Now area of ABC =