Your uncle is making you a desk for you to take to college. one side of the desk is 48 inches and the diagonal length is 53.7 inches. what is the length of the other side of the desk? 12 inches 23.8 inches 17.4 inches 24 inches

Let
a> length of the desk
b> wide of the desk
D> diagonal of the desk

we know that
D=53.7 in
a=48 in
b=?
applying the Pythagoras Theorem
D²=a²+b²
b²=D²-a²> b²=53.7²-48²> b²=579.69> b=√579.69
b=24.08 in> 24 in

the answer is
24 in

We look for the distance between each one of the vertices applying the following formula:
 d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
 For QR:
 QR = root ((4-6) ^ 2 + (-7 + 2) ^ 2)
 QR = 5.385164807
 For QS:
 QS = root ((2-6) ^ 2 + (-5 + 2) ^ 2)
 QS = 5
 For RS:
 RS = root ((2-4) ^ 2 + (-5 + 7) ^ 2)
 RS = 2.828427125
 Now we apply the heron formula:
 A = root (s * (s-a) * (s-b) * (s-c))
 Where,
 s = (a + b + c) / 2
 s = (5.385164807 + 5 + 2.828427125) / 2
 s = 6.606795966
 Substituting:
 A = root (6.606795966 * (6.606795966-5.385164807) * (6.606795966-5) * (6.606795966-2.828427125))
 A = 7.00000000
 A = 7 units ^ 2
 
 The area, in square units, of triangle QRS is:
 A = 7 units ^ 2