Question

The diagonal of rectangle ABCD measures 2 inches in

length.
B
C
60°
2
30%
D
What is the length of line segment AB
O 1 inch
O√3 inches
O4 inches
O 4√3 inches

Answer 1

AB = √3 inches

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
`x:x√(3):2x`

• 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

`\implies \textsf{AD} = 2x`

As AD = 2 then:

`\implies 2 = 2x \implies x = 1`

AB = CD which is opposite angle 60°, so:

`\implies \textsf{AB} = x√(3)=√(3)`