Mathematics Question and Solution
Calculating Area Yellow.
Let y be each of the two equal lengths that makes the length of the ascribed rectangle.
Calculating Yellow Area.
a = 14+18
a = 32 units.
a is the width of the ascribed rectangle.
b = 2y units.
b is the length of the ascribed rectangle.
c² = 32²+y²
c = √(1024+y²) units.
d² = 14²+(2y)²
d = √(196+4y²) units.
e² = 18²+y²
e = √(324+y²) units.
Therefore;
√(324+y²)² = √(196+4y²)²+√(1024+y²)²-2√(1024+y²)*√(196+4y²)cosx
324 = 4y²+1220-2√(1024+y²)*√(196+4y²)cosx --- (1).
cosx = 32/√(1024+y²) --- (2).
Substituting (2) in (1).
324 = 4y²+1220-2√(1024+y²)*√(196+4y²)(32/√(1024+y²))
324 = 4y²+1220-64√(196+4y²)
64√(196+4y²) = 4y²+896
16√(196+4y²) = y²+224
256(196+4y²) = y⁴+448y²+50176
50176+1024y² = y⁴+448y²+50176
1024y²-448y² = y⁴
y⁴ = 576y²
y² = 576
y = 24 units.
Recall.
b = 2y
And y = 24 units.
b = 2*24
b = 48 units.
b is the length of the ascribed rectangle.
Therefore Yellow Area is;
(48*32)-½(14*48)-½(32*24)
= 1536-336-384
= 816 square units.
