In the figure above, $A B C D$ is a rectangle. If $A D = 6$ , which of the following could be the length of $¯ ¯¯¯¯¯¯ ¯ A C$ ?

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Solution

The correct option is E $7$
In triangle $A C D,$ angle $A D C$ is greater than the other two angles

By sine rule , we get $\frac{A C}{A D} = \frac{∠ (A D C)}{∠ (D C A)}$

We know that $∠ (A D C) > ∠ (D C A)$

Therefore $A C > A D = 6$

Therefore option $E$ is correct

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Q. In the figure above,

A C = 6

and

B C = 3

. Point

P

(not shown) lies on

A B

between

A

and

B

such that

C P ⊥ A B

. Which of the following could be the length of

C P

Q. If A(-3, 5), B(0, -4), C(6, -2), and D(3, 7), find the area of the rectangle ABCD.

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In the figure above, ABCD is a rectangle. If AD=6, which of the following could be the length of ¯¯¯¯¯¯¯¯AC?

The correct option is E 7In triangle ACD, angle ADC is greater than the other two anglesBy sine rule , we get ACAD=∠(ADC)∠(DCA)We know that ∠(ADC)>∠(DCA)Therefore AC>AD=6Therefore option E is correct

In the figure above, $A B C D$ is a rectangle. If $A D = 6$ , which of the following could be the length of $¯ ¯¯¯¯¯¯ ¯ A C$ ?

The correct option is E $7$
In triangle $A C D,$ angle $A D C$ is greater than the other two angles

By sine rule , we get $\frac{A C}{A D} = \frac{∠ (A D C)}{∠ (D C A)}$

We know that $∠ (A D C) > ∠ (D C A)$

Therefore $A C > A D = 6$

Therefore option $E$ is correct