Certainly! Let's solve this step by step.
1. Define the variables:
- Let [tex]\( x \)[/tex] be the length of the rectangle in meters.
- Then the width of the rectangle is [tex]\( x + 7 \)[/tex] meters, as it is 7 meters greater than the length.
2. Express the area in terms of [tex]\( x \)[/tex]:
- The area [tex]\( A \)[/tex] of the rectangle is given as the product of its length and width.
- Therefore, the area [tex]\( A = \text{length} \times \text{width} \)[/tex].
- Given the area is 170 square meters:
[tex]\[
x \times (x + 7) = 170
\][/tex]
3. Set up the equation:
- Expand the product on the left-hand side:
[tex]\[
x^2 + 7x = 170
\][/tex]
4. Write the quadratic equation in standard form:
- To have the quadratic equation in standard form [tex]\( ax^2 + bx + c = 0 \)[/tex], we need to bring all terms to one side of the equation:
[tex]\[
x^2 + 7x - 170 = 0
\][/tex]
So, the quadratic equation in standard form that represents the area of the rectangle is:
[tex]\[
x^2 + 7x - 170 = 0
\][/tex]
