Asquare has a side length of 12 cm. Which of the following is closest to the length of its diagonal?

Answer 1

Hello Aanylah! This is a perfect example of a special triangle problem known as the "1-1-sqrt(2)", where there is a right triangle with two 45-degree angle measures, and "sqrt(2)" is the hypotenuse. Technically, you can always use the Pythagorean Theorem to get the answer (a²+b²=c²), but it's faster to remember this particular triangle's measurements.

Consider a triangle with sides that match your square, in this case 12cm. Since you have a square, you know that this is a right-triangle. Having two sides with equal lengths means that the angles of those must measure equally... 45-degrees.

If you apply the 1-1-sqrt(2) rule, then you can treat this triangle as a scaled version of that. This gives you a triangle measuring "1x(12) - 1x(12) - sqrt(2) x (12)". This means your hypotenuse (the diagonal of the square) is equal to 12xsqrt(2), or approximately 16.97 cm.

Answer 2

the diagonal is the hypotenuse of a right triangle with sides 12 and 12

d^2 = 12^2 + 12^2 = 144+ 144 = 2(144)

d = 12sqr2 = about 16.97 or 17 cm. rounded off to nearest integer or 17.0 rounded off to nearest decimal. either way it's 17 cm.