The length of a rectangle is seven feet more than its width. The area of the rectangle is four...

Question:

The length of a rectangle is seven feet more than its width. The area of the rectangle is four hundred ninety-four square feet. What equation could you use to get the dimensions of the rectangle?

Sides and Area of a Rectangle:

A Rectangle is a two-dimensional closed planner geometry that has four right angles at each vertex and out of four sides, opposite sides are parallel and equal in length.

It has two diagonals made by joining the opposite vertices and both the diagonals have the same length.

A rectangle satisfies the Pythagorean theorem and diagonal length is calculated by using the Pythagorean theorem-

If the length and width of a rectangle are L and W then its diagonal length-

{eq}\displaystyle D^{2} = L^{2}+W^{2} {/eq}

where D is the diagonal length

Area

formula-

{eq}\displaystyle A = L \times W {/eq}

here A is the area of the rectangle

Given that the length of a rectangle is seven feet more than its width.

{eq}\displaystyle L = 7+W --------(1) {/eq}

Also given that the area of the rectangle is four hundred ninety-four square feet.

{eq}\displaystyle A = 494 ~ft^{2} {/eq}

{eq}\displaystyle L \times W = 494 {/eq}

now put the value of L from the equation(1)-

{eq}\displaystyle (7+W)W = 494 {/eq}

{eq}\displaystyle W^{2}+7W-494 = 0 {/eq} is the equation that can be used to find the dimensions of the rectangle.