if the length of the diagonal of a square is 10, what is the area of the square?

Question

the answer choice are 10 or 25 or 50 or 75 or 100.

Answer 1

Hi, Amy.

 

okay, so we know that for a right triange, a² + b² = c²

So the triangle formed by two adjacent sides of the square and the diagonal is a right triangle with sides length X.

Therefore, 

X² + X² = 10² (since both the legs of the triangle are equal)

2X² = 100

X^{2 =} 50

X = 5√2  = length of each leg of triangle and also the length  of the sides of the square.

Therefore for the area of the square:

5√2 x 5√2 = 50

Therefore , the area of the square is 50 square units

 

Answer 2

The diagonal cuts the square into two equal right triangles, and a and b are equal because it's a square with 4 equal sides.

 

a² + a² = 10²

2a² = 100

a² = 50

 

Hey, isn't the area the length of a side squared? Then our area is 50.

Answer 3

If the diagonal is 10 then the side is 5√2 (because in an isosceles right triangle the ration of the hypotenuse to the side is

√2:1)

 

The area of the triangle is (5√2)² (1/2) = 25