Ina n isosceles triangle ABC, AB = AC and AD is perpendicular to BC at D. If AD = 8 cm and perimeter of ΔABC is 64 cm, then the area of ΔABC is:
Answer & explanation
Correct answer: option 3
Let, AB = AC = x
BD = y
We know that,
Perimeter is the total sum of all the sides.
BD = DC
According to the question,
x + x + y + y = 64
x + y = 32
x = 32 - y
From ΔABD,
x2 = y2 + 82
(32 - y)2 = y2 + 82
322 - 64y + y2 = y2 + 64
64y = 1024 - 64
y = 15 = BD
Now,
BC = 2 × BD = 2 × 15 = 30 cm
Area of triangle ABC = \(\frac{1}{2}\) × 30 × 8 = 120 cm2