Theory question 103
Mensuration of Plane Shapes(a) The diagonals of a rhombus are 10.2 cm and 9.3 cm long. Calculate, correct to one decimal place, the perimeter of the rhombus.
(b) Given that sin x = ⅗, 0° < x < 90°, find the value of 5 cos x − 4 tan x.
Show the model answer
Model answer
(a) Diagonals bisect at right angles: half-diagonals 5.1 cm and 4.65 cm
Side = √(5.1² + 4.65²) = √47.6325 ≈ 6.902 cm
Perimeter = 4 × 6.902 ≈ 27.6 cm
(b) Sides 3, 4, 5: cos x = 4/5, tan x = 3/4
5 cos x − 4 tan x = 4 − 3 = 1
Explanation
A rhombus's diagonals cut each other in half at right angles.