Mathematics Question and Solution
Calculating k.
Notice.
115.5 square units is the area of rectangle ABCD.
AD = (2k+6) units.
AD is the length of rectangle ABCD.
a²+6² = (4k)²
a² = 16k²-36
a = √(16k²-36) units.
b = a+k
b = (√(16k²-36)+k) units.
b is CD, the width of rectangle ABCD.
It implies;
(AD) * (CD) = 115.5
Calculating k.
tanc = k/2k
c = atan(½)°
d = 2c
d = 2atan(½)°
e = 90-d
e = (90-2atan(½))°
Therefore;
sin(90-2atan(½))° = 6/4k
k = 6/(4sin(90-2atan(½)))
k = 2.5 units.
Checking Accuracy.
Recall.
(AD) * (CD) = 115.5
And k = 2.5 units.
(2k+6)(√(16k²-36)+k) = ?
((2*2.5)+6)(√(16(2.5)²-36)+2.5) = ?
(11)(10.5) = 115.5 square units.
Again, k is 2.5 units.
