The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle.

Asked by chsrvsh | 24th Jul, 2019, 09:29: PM

Expert Answer:

Let x be the equal sides of an isoscels triangle and 2y be the unequal side of an isosceles triangle.
Let AD be the altitude. AD = 8 cm
perimeter of isosceles triangle = 32 cm
2x + 2y = 32
x + y = 16
x = 16 - y....(i)
In ΔADB,
AD2 + DB2 = AB2 
82 + y2 = x2 ....(ii)
Solving (i) and (ii) we get x = 10 and y = 6
Hence, base of an isosceles triangle is 12 cm
Area of triangle = 1/2 × 8 × 12 = 48 cm2

Answered by Sneha shidid | 25th Jul, 2019, 10:13: AM