Answer:
AB = √3 inches
Step-by-step explanation:
As ABCD is a rectangle:
- AB = CD
- AD = BC
- ∠ABC = ∠CDB
- ∠ADB = ∠CBD
From inspection of the diagram, the two congruent triangles formed by the diagonal are 30-60-90 triangles.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio of [tex]x:x\sqrt{3}:2x[/tex]
- x is the side opposite the 30° angle
- x√3 is the side opposite the 60° angle
- 2x is the side opposite the right angle
AD is opposite the right angle
[tex]\implies \textsf{AD} = 2x[/tex]
As AD = 2 then:
[tex]\implies 2 = 2x \implies x = 1[/tex]
AB = CD which is opposite angle 60°, so:
[tex]\implies \textsf{AB} = x\sqrt{3}=\sqrt{3}[/tex]
