Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the width of the rectangle be x and the length be y.
Let the unknown inscribed length of the rectangle be z.
Calculating z.
√(74)²+√(58)²=√(34)²+z²
Therefore z is;
z = √(98) units.
Calculating x (width).
x² = 156-2√(98)*√(58)cos68.2
x² = 100.003444042
x = 10.0001722006 units.
Calculating y (length).
y = √(34)cos30.9651378262 + √(58)cos23.199577149
y = 11.999876013 units.
Therefore area rectangle is;
xy
= 10.0001722006*11.999876013
= 120.000826516 square units.
Calculating area yellow.
It is;
Area triangle with two length √(34) units and √(58) units, and angle (180-30.9651378262-23.199577149)
= ½(√(34)*√(58))sin125.835285025
= 18.0005372507 square units.
Area yellow ÷ Area rectangle is;
18.0005372507 ÷ 120.000826516
= 0.15000344392
= 0.15
15/100
= 3/20
