Choose w to represent the width because the length is described by referring to the width: it's 3 more than (add 3) triple (multiplied by 3) the width.

Length = 3w + 3

The diagonal forms two right triangles, each with leg = w, other leg = 3w + 3, hypotenuse = 13.

The Pythagorean Theorem says $(\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2$ so

$w^2+(3w+3)^2=13^2\\\\w^2+9w^2+18w+9=169\\\\10w^2+18w-160=0\\\\5w^2+9w-80=0\\$

Now solve using the Quadratic Formula with $a=5,\,b=9,\,c=-80$ .

$w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-9\pm\sqrt{81+1600}}{10}\\\\w=\frac{-9\pm\sqrt{1681}}{10}\\\\w=\frac{-9\pm41}{10}\\\\w=-5\text{ or }w=3.2$

The negative root makes no sense as a distance, so the width of the rectangle is 3.2 cm. The length is 3(3.2) + 3 = 12.6 cm.

5 0

2 years ago

Calculate the slope of the line passing through the two colored points below. (1,4) (-1,-1)

leonid [27]

Answer:

Slope = $\frac{5}{2}$

Step-by-step explanation:

We can define the slope as the "change in y values" divided by the "change in x values".

By change in, we mean, 2nd point MINUS the first point values.

The points given is:

(1,4) & (-1,-1)

Change in y value:

-1 - 4 = -5

Change in x value:

-1 -1 = -2

Slope is -5/-2 = 5/2

There is no answer choice. The correct answer is 5/2

6 0

3 years ago

Which of these daily activities helps build a stronger body?

Whitepunk [10]

Answer:

riding a bicycle to and from school each day

Step-by-step explanation:

As this involves the constant application of force from the leg muscles, this will help to build a stronger body.

8 0

1 year ago

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