Question

7: In the adjoining figure, all measurements are in centimetres.
Find the perimeter of the quadrilateral ABCD.
bebas​

Answer 1

Answer:

perimeter of a triangle.

ac² = ab² + bc²

ac² = 8² + 6²

ac² = 64 + 36

ac² = 100

ac² = √100

ac = 10

therefore ac is 10cm

let the center point of diagonal be o

ad = dc

half of ac is 5cm

ad² = ao² + od²

ad² = 5² + 12²

ad² = 25 + 144

ad² = 169

ad = √ 169

ad = 13 cm

Hope it helps you

Answer 2

Answer:

40 cm

Step-by-step explanation:

In triangle ADE and DEC:

DE = DE               (common side)

AD = DC              (given)

AED = DEC          (90)

Using RHS property

ADE ≅ DEC

_____________________________

$AB^2+BC^2=AC^2$

$8^2+6^2= AC^2\\\\64 + 36 = AC^2\\\\AC^2 = 100$

=> AC= 10 cm

as ADE ≅ DEC :-

AE = EC

AE+EC=10

2AE= 10

=> AE , EC = 5 cm

_____________________________

using pythagoras theorem:

$AE^2+ED^2=AD^2$

$5^2+12^2=AD^2$

$AD^2$ = 144+25

AD = √169

AD = 13 cm

as it is given that AD = DC:-

DC = 13 cm

THEREFORE:

Perimeter = 8+6+13+13

= 40

______________________________

Hope it helps

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