Question

ABCD is a parallelogram and this figure is NOT drawn to scale.

Answer 1

The angle does not matter. Think of it as finding the other side to a triangle. Use $a ^{2} +b^2 =c^2$

a=39 (line AB)
b=b (the leg we need to find)
c=89 (line BD)

$39^2 + b^2 = 89^2$
$1521 + b^2 = 7921$
(subtract the 1521 from both sides)
$b^2 = 6400$
(square root both sides)
$\sqrt{(b^2)} = \sqrt{6400}$

b = 80
AD=80

Answer 2

Answer:  The length of AD is 80 cm.

Step-by-step explanation:  Given that ABCD is a parallelogram, where m∠BCD = 90°, AB = 39 cm and BD = 89 cm.

We are to find the value of AD.

We know that

the measures of the opposite angles of a parallelogram are equal.

So, in the parallelogram ABCD, we have

m∠BAD =  m∠BCD = 90°.

So, triangle ABD is a right-angled triangle  with AB and AD as two legs and BD as the hypotenuse.

Using Pythagoras law in triangle ABD, we get

$AB^2+AD^2=BD^2\\\\\Rightarrow AD^2=BD^2-AB^2\\\\\Rightarrow AD^2=89^2-39^2\\\\\Rightarrow AD^2=7921-1521\\\\\Rightarrow AD^2=6400\\\\\Rightarrow AD^2=80^2\\\\\Rightarrow AD=80.$

Thus, the length of AD is 80 cm.