Mathematics Question and Solution
½(xy)=24
xy = 48 ------ (1)
x²+y²=10² ------- (2)
And;
x²+y²=(x+y)²-2xy
Therefore;
(x+y)²-2xy=100
And;
xy = 48
(x+y)²-2(48)=100
(x+y)²=196
x+y=14 ----- (3)
x = 14-y ------ (4)
Substitute (4) in (1)
y(14-y)=48
y²-14y+48=0
(y-7)²=-48+49
y = 7±1
Therefore;
y = 8 units or 6 units.
It implies;
For y = 8 units,
x = 14-y
x = 14-8
x = 6 units.
Calculating r, radius of the inscribed circle.
½(6r)+½(8r)+½(10r)=½(8*6)
3r+4r+5r=24
12r = 24
r = 2 units.
Therefore area of the inscribed circle is;
πr², and r = 2 units.
= π(2)²
= 4π square units.
