Question

area of a square ABCD is 16 sq units and A(2,3) and B(x,5). find the value of x by using distance formula

Answer 1

We have,area of square ABCD = 16 square units

Let the length of each side of square = s units

Now, area = 16 square units⇒s2 = 16⇒s = 4 units Now, we have, AB = 4 units

The coordinates of A and B are A(2,3) and B(x,5)

⇒Now, AB = 4

⇒(x−2)2 +(5−3)2−−−−−−−−−−−−−−−√ = 4

⇒(x−2)2 +(5−3)2 = 16

⇒(x−2)2 + 4 = 16

⇒(x−2)2 = 12⇒x−2 = ±23√

⇒x = 2(3√+1) or x = 2(1−3√)