A parking lot has four sides. One pair of opposite sides are 100 yards long. The other two sides are 60 yards long. The distance from one end of the longer side to the opposite end of the shorter side is 120 yards. Is the parking lot a rectangle? Answer the questions below to find out. 5. If the distances given form a right triangle, which number is the hypotenuse, and why?

6. Which numbers are the two sides?

The parking lot does not form a rectangle.

Step-by-step explanation:

Given: One pair of opposite sides of parking lot are 100 yards long. The other two sides are 60 yards long.

The distance from one end of the longer side to the opposite end of the shorter side is 120 yards.

To find: If the distances given form a right triangle?

Also, to find the hypotenuse and the numbers which represent the two sides.

Solution:

In a triangle, if the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is said to be a  right angled triangle.

So, the triangle is not a right angled triangle.

So, none of the angles of the parking lot forming a quadrilateral is equal to .

Hence, the parking lot is not a rectangle although the opposite sides are equal.

(A quadrilateral in which opposite sides are equal such each angle is is a rectangle )

The distances given do not form a right triangle.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form