What is the length of a diagonal of a square if its area is 98 square feet?
A diagonal of a square divides it into two congruent right-triangles.
Answer: The length of a diagonal of a square with area 98 square feet is equal to 14 feet.
Let's find the length of a diagonal using Pythagoras theorem.
Let's draw a square ABCD of area 98 square feet as shown below
Join the points B and C to construct the diagonal BC
Area of the square = Side2
=> AC2 = 98 (given)
=> AC = √98
=> AC ≈ 9.89949493
Thus, AC ≈ 9.9 feet
Also, AC = AB = CD = BD = 9.9 feet (since, they are the sides of square ABCD)
From the figure we observe that, △BAC is a right angled triangle with ∠A = 90°
Applying Pythagoras theorem to △BAC we get,
(BC)2 = (AC)2 + (AB)2
(BC)2 = 9.92 + 9.92 (Since, AC = AB)
(BC)2 = 98.01 + 98.01
BC = √196.02
BC ≈ 14.00071427
BC ≈ 14.0 feet