Question

In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm².
Find x.

Answer 1

Here, the diagram will be,

We have Pythagoras theorem which states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

Since ABC is an isosceles triangle, therefore perpendicular from vertex will cut the base in two equal segments.

First, we consider the ΔABD, and applying Pythagoras theorem we get,
AB² = AD² + BD²
AD² = x² - 5²
AD² = x² - 25
AD = `sqrt( x^2 - 25 )`                .....(i)
Now,
Area = 60
`1/2 xx 10 xx "AD"` = 60
`1/2 xx 10 xx sqrt( x^2 - 25 )` = 60
x = 13.
Therefore, x is 13 cm.