Question

4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.

[2]
a. Draw a picture of the rectangle
[4]
b. Write an EXACT expression for the base and the height of the rectangle.
[2]
C. Use your expressions to find the EXACT area of the rectangle.

Answer 1

9514 1404 393

Answer:

a) see attachment

b) base: 4, height: 4√3

c) area: 16√3

Explanation:

a) The figure is drawn in the attachment

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b) The side lengths of a 30-60-90 right triangle have the ratio ...

1 : √3 : 2

Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.

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c) The area is the product of base and height:

A = bh

A = 4(4√3) = 16√3 . . . . square units