What is the length of a diagonal of a square if its area is 98 square feet?
Solution:
A diagonal of a square divides it into two congruent right-triangles.
Let's find the length of a diagonal using the Pythagoras theorem.
Let's draw a square ABCD of area 98 square feet as shown below
Join 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)2 =196.02
BC = √196.02
BC ≈ 14.00071427
BC ≈ 14.0 feet
Thus, the length of a diagonal of the square with an area of 98 square feet is equal to 14 feet.
What is the length of a diagonal of a square if its area is 98 square feet?
Summary:
The length of a diagonal of the square with an area of 98 square feet is equal to 14 feet.