Answer:
The value of CD is 2√5
Step-by-step explanation:
* Lets describe the figure to know its name
- ABCD is a quadrilateral
∵ BC parallel to AD
∵ BC = 6 units and AD = 8 units
- The quadrilateral which has two parallel sides not equal in length is a
trapezoid
∴ ABCD is a trapezoid, where BC and AD are its bases
∵ BA perpendicular to AD
∴ BA is the height of the trapezoid
- The area of the trapezoid = 1/2 (base 1 + base 2) × its height
∵ The bases of the trapezoid are BC and AD
∵ BC = 6 and AD = 8
∵ Its area = 28 units²
∴ 1/2 (6 + 8) × height = 28
∴ 1/2 (14) × height = 28
∴ 7 × height = 28 ⇒ divide both sides by 7
∴ height = 4
∵ The height is BA
∴ BA = 4 unit
- To find the length of CD draw a perpendicular line from C to AD and
meet it at E
∵ BA and CE are perpendicular to AD
∴ BA // CE
∵ BC // AD
- Perpendicular lines between parallel lines are equal in lengths
∴ BA = CE and BC = AE
∵ BA = 4 and BC = 6
∴ CE = 4 and AE = 6
∵ AD = 8 units
∵ AD = AE + ED
∴ 8 = 6 + ED ⇒ subtract 6 from both sides
∴ ED = 2 units
- In ΔCED
∵ m∠CED = 90°
∴ CD = √[(CE)² + (ED)²] ⇒ Pythagoras theorem
∵ CE = 4 and ED = 2
∴ CD = √[(4)² + (2)²] = √[16 + 4] = √20 = 2√5
* The value of CD is 2√5
