Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
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.
Answer
Answer (as printed):
Explanation
Let ABC be the isosceles triangle and AD be the altitude. Let AB = AC = x. Then, BC = (32 – 2x). Since, in an isosceles triangle, the altitude bisects the base, so BD = DC = (16 – x). In ∆ ADC, AC2 = AD2 + DC2 ⇒ x2 = (8)2 + (16 – x)2 ⇒ 32x = 320 ⇒ x = 10. ∴ BC = (32 – 2x) = (32 – 20) cm = 12 cm. 1 1 2 2 Hence, required area = × BC × AD = × 12 × 10 cm = 60 cm . 2 2
Explanation as extracted from the printed page; notation may be imperfect.