# 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.

**Explanation:**

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 = Side^{2}

=> AC^{2} = 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 } = 9.9^{2} + 9.9^{2} (Since, AC = AB)

(BC)^{2} = 98.01 + 98.01

(BC)^{2} =196.02

BC = √196.02

BC ≈ 14.00071427

BC ≈ 14.0 feet