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❖ Given ❖
- ABCD is a quadrilateral
- AB = 9 cm
- AD = 15 cm
- ∠ ABD = 90°
- CE ⏊ BD
- Ar (ABCD) = 72 cm²
❖ To find ❖
- Length of CD = ?
❖ Solution ❖
Using Pythagorean theorem in ∆ ABD
➹ AD² = AB² + BD²
➹BD² = AD² - AB²
➹BD² = (15)² - (9)²
➹BD² = 144
➹ BD = 12 cm
Now,
As we know
ar (∆) = 1/2×base ×height
so,
ar (∆ ABD) = 1/2 × AB × BD
ar (∆ ABD) = 1/2 × 9 × 12
ar (∆ ABD) = 54 cm²
Now,
as given that area of ABCD is 72 cm²
so,
ar (∆ CBD) = ar(ABCD) - ar (∆ ABD)
ar ( ∆ CBD) = ( 72 - 54 ) cm²
ar (∆ CBD) = 18 cm²
Then
also
ar (∆ CBD) = 1 /2 × BD × CE
18 cm² = 1 / 2 × 12 × CE
■ CE = 3 cm (Ans.)
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