The length of the rectangle is x cm. The length of a diagonal of the rectangle is 8 crn. The perimeter of the rectangle is 20 cm. Show that ia + 91 +b=0 where a and b are integers to be found.​

a = -10 and b = 18.

Step-by-step explanation:

Let w represent the width of the rectangle.

We are given that the perimeter of the rectangle is 20 cm, this means that:

Let's put w in terms of x. Divide both sides by two:

And solve for w:

So, the rectangle measures x by (10 - x) cm.

According to the Pythagorean Theorem:

a and b are the legs and c is the hypotenuse.

Substitute x for a, w for b, and 8 for c:

Simplify and substitute:

Square:

Isolate the equation. So:

Since the leading coefficient is one, divide both sides by two:

Therefore, a = -10 and b = 18.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."