Mathematics Question and Solution
Considering similar plane shapes (triangle) ratios;
10 = y
(16+x) = x
Cross multiply and making y the subject of the formula.
y = 10x/(16+x) ----- (1)
And;
24+½(xy) = ½)10x) ----- (2)
Substituting (1) in (2)
It implies;
24 + ½(x(10x/(16+x))) = ½(10x)
24 +(5x²/(16+x)) = 5x
5x² = (5x-24)(16+x)
5x² = 80x+5x²-384-24x
384 = 56x
x = 48/7 units.
Therefore;
y = 10(48/7)/(16+(48/7))
y = (480/7)/(160/7)
y = 48/16
y = 3 units.
It implies;
Area yellow (area trapezoid) is ;
Area trapezoid with parallel sides 10 units and 3 units respectively and height 16 units.
= ½(10+3)*16
= 13*8
= 104 square units.
