# problem solving in RAE

posted by Jee-Anne

What is the area of a rectangle whose length is 1 unit longer than its width and whose diagonal is 2 unit longer than the width?

1. Reiny

looks like Pythagoras.

width --- x
length --- x+1
diagonal --- x+2

x^2 + (x+1)^2 = (x+2)^2

by recognition:
the sides are one unit apart, the only Pythagorean triple like that is 3,4,5, since 3^2 + 4^2 = 5^2.

If you did not recognize that:
x^2 + x^2 + 2x + 1 = x^2 + 4x + 4
x^2 - 2x - 3 = 0

(x - 3)(x+1) = 0
x = 3 or x = -1, but a side can't be negative, so

x = 3
find the area using base*height

## Similar Questions

1. ### algebra , help

Can someone help me set up the equations thanks. Directions: Solve each of the following applications. Give all answers to the nearest thousandth. Problem: Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal …
2. ### basic geometric

10. a rectangle has width the same as a side of a square whose perimeter is 20m. the length of the rectangle is 9m. find the perimeter of this rectangle. 34. The width of a rectangular picture is one-half the length. The perimeter …
3. ### basic geometry

A rectangle has width the same asa a side of a square whose perimeter is 20m.the length of the rectangle is 9m. Find the perimeter of this rectangle. 34. The with of a rectangular picture is on-half the length . The perimeter of the …
4. ### Geometry

The length of a rectangle is 1cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions(the length and the width)of the rectangle?
5. ### College Math II

Write a complete solution to each problem. If the length of a rectangle is 3 feet longer than the width and the diagonal I s 15 feet, then what are the length and width?
6. ### Math ( Algebra 1 )

Two rectangles have the same width. The length of one is 2 feet longer than the width. The length of the other is 4 feet longer than the width. The larger rectangle has 8 more square feet than the smaller. What is the width of the …
7. ### algebra

Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 5 more square feet than the smaller. What is the width of the …
8. ### math

Two rectangles have the same width. The length of one is 2 feet longer than the width. The length of the other is 4 feet longer than the width. The larger rectangle has 8 more square feet than the smaller. What is the width of the …
9. ### Math

Find the area of a rectangle whose length is more than its width and the width is equal to the side of a square whose area is 144.
10. ### math

a wire whose length is at most 114cm,is bent to form a rectangle.If the length of the rectangle is 5cm longer than the width, what is the maximum area of the rectangle?

More Similar Questions