Question

Find the length of OB and AC
Show working out

Answer 1

√13 units

Explanation:

a² + b² = c²

Use this equation. This rectangle is made up of two right triangles, so you can use the Pythagorean theorem.

Considering this is a rectangle, OB and AC should be the same value. Let's use the right bottom triangle to solve this.

You know from the graph the values of a and b.

Line OA is 3 units long, and Line AB is 2 units long.

These 2 values are your a and b, so just plug them into the equation.

3² + 2² = c²

9 + 4 = 13

set c² equal to 13.

c² = 13

To get rid of the square sign, square root both sides of the equation. The square sign gets canceled out and this is your answer.

c = √13

Answer 2

OB = AC = sqrt(13)

Explanation:

OB² = OA² + AB²

OB² = 3² + 2² = 9 + 4

OB² = 13

OB = sqrt(13)

AC = OB (diagonals of a rectangle are equal in length)