Question

ABCD is a parallelogram, AE DC and CF AD. lfAB= 16 cm, AE = 8 cm and CF = 10 cm, find AD. In Fig. 9.15.​

Answer 1

Answer:

Given,

AB = CD = 16 cm (Opposite sides of a parallelogram)

CF = 10 cm and AE = 8 cm

Now,

Area of parallelogram = Base × Altitude

= CD×AE = AD×CF

⇒ 16×8 = AD×10

⇒ AD = 128/10 cm

⇒ AD = 12.8 cm

Explanation:

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Answer 2

Information provided in given question :

• ABCD is a parallelogram
• AE is perpendicular with DC
• CF is perpendicular with AD
• AB= 16 cm
• AE = 8 cm
• CF = 10 cm

What we have to find out :

• We have to find out the AD

Solution with proper explantion :

According to the figure

• AB = CD = 16 cm

(∵ Opposite sides of parallelogram are equal )

• CF = 10 cm

• AE = 8 cm

Now ,

Area of parallelogram

• ➡ Base × Altitude

Here for base CD , AE is altitude or height and

Here for base AD , CF is altitude or height

Put the given value in formula and solve it :

$\rm \implies \: CD \times AE = AD \times CF$

$\rm \implies \: 16 \times 8 = AD \times 10$

$\rm \implies \: 128 = AD \times 10$

$\rm \implies \: AD = \dfrac{128}{10}$

$\rm \implies \: AD = 12.8 \: cm$

Therefore,

• The AD = 12.8 cm is the required answer

Note :

• Refer the attachment to read second alternative method to solve this example