Respuesta :
the area of the rectangle is 80. 1 cm²
What is the area of a rectangle?
From the given information, let's say one side of rectangle = a
The other side = (36 - 2a)/2
= 18 - a cm
The angles between the diagonals of the rectangle is 78°
Then, the angle diagonal has with base will give
= (180° - 78°)/2
= 102/2
= 51°
We have the angle to be 51 degrees, using the tan ratio
Tan θ = opposite/ adjacent
Opposite of angle 51 degrees = a
Adjacent = 18 - a
Thus,
[tex]tan 51 = \frac{a}{18 - a}[/tex]
[tex]1. 2349 = \frac{a}{18-a }[/tex]
cross multiply
[tex]18 -a ( 1. 2349) = a[/tex]
[tex]22. 23 - 1. 2349a = a[/tex]
collect like terms
[tex]a + 1. 2349a = 22. 23[/tex]
[tex]2. 2349 a = 22. 23[/tex]
[tex]a = \frac{22. 23}{2. 2349}[/tex]
a = 9. 95
If a = 9. 95cm
Then, 18 - a = 18 - 9. 95 = 8. 05cm
The formula of area of a rectangle is given as;
Area = width × length
Area = 9.95 x 8.05
Area = 80. 1 cm²
Thus, the area of the rectangle is 80. 1 cm²
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