The given square has a diagonal of 24 meters. What is the measure of a side length? Round to the nearest tenth, if necessary

Question

asked May 25, 2019 112k views

2 Answers

Kypk · Answer 1 · 2019-05-29T10:17:48+0000

Answer:

Side of the square ≅
16.97

Explanation:

The diagonal of a square with side 'a' makes right angled Isosceles triangle.

The Diagonal becomes hypotenuse of the triangle i.e 24 m (given)

Using Pythagorean Theorem:

(Hypotenuse)^2=(Perpendicular)^2+(Base)^2

As, Perpendicular and base of the triangle is equal in case of a square with a side of 'a'

$H^2=a^2+a^2\\\\24^2=2a^2\\\\2a^2=576\\\\a^2=288\\\\a=√(288) \\\\$ ≅
16.97

OR, (Alternate method)

Diagonal of a square =
√(2)*a

:
√(2) =1.414

$24=√(2)*a\\\\ 24=1.414*a\\\\a=(24)/(1.414) \\\\a=16.973$