Question 175285
Let x = amount decreased
.
"area of new" = 1/2("area of original")
.
(15-x)(20-x) = 1/2(15)(20)
Applying FOIL to the left:
300-15x-20x+x^2 = (15)(10)
x^2-35x+300 = 150
x^2-35x+150 = 0
Factoring:
(x-30)(x-5) = 0
.
Two possible solutions:
x = {5, 30}
.
We can toss out the 30 because we'll get negative measurements.
Therefore,
x = 5 cm
.
Dimensions:
(15-5)cm by (20-5)cm
or
10cm by 15cm