In an isosceles triangle ABC with AB = AC and AD is perpendicular to BC, if AD = 6 cm and the perimeter of ΔABC is 36 cm, then the area of ΔABC is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 48 cm2
| Understanding | Application |
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In the isosceles triangle, the perpendicular from one vertex bisects the respective side. The area of a triangle is (1 / 2) × base × height. |
⇒ AB = AC In ∆ABC, the perimeter of ABC will be ⇒ AB + BC + AC = 36 Let AB = AC = y, and BD = DC then the perimeter will be ⇒ y + y + BC = 36 ⇒ BC = 36 - 2y ⇒ BD = 18 - y By applying the pythogorus theorem in ∆ABD ⇒ y2 = 36 + (18 - y)2 ⇒ 36y = 360 ⇒ y = 10cm BC = 36 - 20 = 16cm The area of ∆ABC = (1/2) × BC × AD ⇒ (1/2) × 16 × 6 ⇒ 48cm2 |