Question

A rectangular painting has a diagonal measure of 25 inches and an area of 168 square inches. Use the formula for the area of a rectangle and the Pythagorean Theorem to find the length and width of the painting.

Answer 1

h^2=x^2+y^2 and xy=168 so y=168/x

625=x^2+28224/x^2

625=(x^4+28224)/x^2

x^4-625x^2+28224=0

I'll use the quadratic because this is a big number :P

x^2=(625±√(277729))/2

x^2=(625±527)/2

x^2=49

x=7

168/7=24

So the dimensions of the painting is 7 inches by 24 inches.