Question

The base BC of an isosceles triangle is 28cm and AB=AC = 50cm and AD ⊥ BC, find the length of AD and area of ΔABC

Answer 1

Given :

• In ΔABC :
• BC = 28cm
• AB = AC = 50cm
• AD ⊥ BC

To find :

• Length of AD
• Area of ΔABC

Solution :

• In ΔADC:
• ∠ADC = 90°            (Right angled)
• AD² = AB² - BD²       (Pythagoras Theorem)
• AD² = 50² - 14²
• AD² = 2500 - 196
• AD² = 2304
• AD = √2304
• AD = 48

★ We took BD length as 14cm , because BC length is 28cm ★

✶ BD = BC/2 ✶

• Area of ΔABC :
• ½ × b × h
• ½ × 28 × 48
• 672

★ Area of ΔABC = 672cm² ★