SOLUTION: The diagonal of a rectangle is 3 ft longer than the length of the rectangle and 4 ft longer than twice the width. Find the dimensions of the rectangle.
Algebra ->
Rectangles
-> SOLUTION: The diagonal of a rectangle is 3 ft longer than the length of the rectangle and 4 ft longer than twice the width. Find the dimensions of the rectangle.
Log On
Question 1131622: The diagonal of a rectangle is 3 ft longer than the length of the rectangle and 4 ft longer than twice the width. Find the dimensions of the rectangle. Found 2 solutions by MathLover1, ikleyn:Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!
if the diagonal of a rectangle is ft longer than the length of the rectangle and ft longer than the width , we have
=>
=>
=>
Find the dimensions of the rectangle:
we can only do this
because neither perimeter nor area is given
One equation is
L = 2W + 1, (1)
as the tutor @LoverMath1 derived in her post.
The other equation is
= 2W + 4.
which follows from the condition.
This second condition, due to (1), is the same as
= 2W + 4. (2)
Equation (2) is your basic equation to solve. Square both sides
W^2 + 4W^2 + 4W + 1 = 4W^2 + 16W + 16
W^2 - 12W - 15 = 0.
Answer. The dimensions of the rectangle are W = and L = 2W+1 = feet.
