Question

HALP.ME

I'm not really sure how to attempt this equation


In quadrilateral ABCD, we have AB=3, BC=6, CD=4, and DA=4.

If the length of diagonal AC is an integer, what are all the possible values for AC? Explain your answer in complete sentences.

Answer 1

Answer: The length of AC can be 4, 5, 6, 7.

Explanation:

Since we have given that

In ABC,

As we know that "Sum of two sides is always greater than the third side",

So,

$3+6>x\implies 9>x\\x+3>6\implies x>3\\x+6>3\implies x>-3$

Similarly,

in ADC,

As we know that "Sum of two sides is always greater than the third side",

$4+4>x\implies 8>x\\4+x>4\implies x>0$

So, from two triangles, we get

Length of AC will be

$3<x<8$

Hence, the length of AC can be 4, 5, 6, 7.