A square has an area of 169 square feet, What is the length of its diagonal, and round it to the tenths place.

Answer 1

Let X be the length of the sides.

Area = X² = 169

Solve for X: X = √169 = 13

Two adjacent sides and the diagonal form a right triangle with the diagonal as the hypotenuse (H).

H² = X² + X² = 2X² (pythagorean theorem)

H = √X² x √2 = 13 x 1.414 = 18.4 ft

Answer 2

13sqr2 = about 13(1.414) = about 18.385 = about 18.4 to nearest tenth

square with area 169 ft^2 has sides 13 feet each

diagonal of a right triangle with base = height = 13 is 13sqr2

diagonal = sqr(13^2 +13^2) = sqr(2(13^2) = 13sqr2

using the pythagorean theorem

the diagonal of a square is the hypotenuse of a right isosceles triangle with two triangle legs = side of the square