Question

A rectangle or piece of paper has a width is 3 inches less than its link it is cut in half along a diagonal to create two congruent right triangles with areas of 44 in.²

Answer 1

The length and width of the rectangle is 11 in and 8 in respectively.

Explanation:

Given,

The width of a rectangle is 3 in less than the length.

The area of each congruent right angle triangle = 44 in²

To find the length and width of the rectangle.

Formula

The area of a triangle with b base and h as height =
`(1)/(2)`bh

Now,

Let, the width = x and the length = x+3.

Here, for the triangle, width will be its base and length will be its height.

According to the problem,

`(1)/(2)`×(x+3)×x = 44

or,
`x^(2) +3x = 88`

or,
`x^(2) +3x-88 = 0`

or,
`x^(2)`+(11-8)x-88 = 0

or,
`x^(2)`+11x-8x-88 =0

or, x(x+11)-8(x+11) = 0

or, (x+11)(x-8) = 0

So, x = 8 ( x≠-11, the length or width could no be negative)

Hence,

Width = 8 in and length = 8+3 = 11 in