Mathematics, 21.09.2019 18:00, taylorrcho977

The diagonal of a rectangle is 15 cm, and the perimeter is 38 cm. what is the area?

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answered: jaquonb23

The area of the rectangle is 68.16 cm²

A rectangle is a quadrilateral in which opposite sides are parallel and equal. Also each angle is a rectangle measures 90°.

Since the diagonal is 15 cm, hence let x represent the length of the rectangle and y represent the width of the rectangle. Hence:

x² + y² = 15²

x² + y² = 225 (1)

The perimeter of the rectangle is 38 cm, hence:

Perimeter = 2(x + y)

38 = 2(x + y)

x + y = 19

y = 19 - x (2)

x² + (19 - x)² = 225

x² + 361 - 38x + x² = 225

2x² - 38x + 136 = 0

x = 14.2 and y = 4.8

Area of the rectangle = xy = 14.2 * 4.8 = 68.16 cm²

The area of the rectangle is 68.16 cm²

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answered: triggercell

68 cm²

Step-by-step explanation:

Area = length × width

Let the width be represented by w and the length be represented by L.

Pythagorean Theorem: w² + L² = diagonal² ⇒ w² + L² = 15²

Perimeter = 2w + 2L ⇒ 38 = 2w + 2L

19 = w + L divided both sides by 2

19 - w = L subtracted w from both sides

Substitute L with 19 - w in the Pythagorean Theorem equation:

w² + (19 - w)² = 15²

w² + 361 - 38w +w² = 15²

2w² - 38w + 361 = 225

2w² - 38w + 136 = 0

w² - 19w + 68 = 0 divided both sides by 2

Use Quadratic Formula to solve for w:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\w=\dfrac{19\pm \sqrt{(-19)^2-4(1)(68)}}{2}\\\\w=\dfrac{19\pm \sqrt{361-272}}{2}\\\\w=\dfrac{19\pm \sqrt{89}}{2}\\\\w=\dfrac{19\pm 9.434}{2}\\\\w=\dfrac{28.434}{2}\quad or\quad \dfrac{9.566}{2}\\\\w=14.217\quad or\quad 4.783\\\\$

Use the Perimeter equation to solve for L:

19 - w = L 19 - w = L

19 - 14.217 = L 19 - 4.783 = L

4.783 = L 14.217 = L

Notice that we end up with the same dimensions regardless of which value we use for w

Now, let's find the Area:

A = L × w

= 14.217 × 4.783

= 68

answered: Guest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

$\frac{ab}{bc} =\frac{ad}{ab}$

now, we can cross multiply

and we get

$ab\timesab=ad\times bc$

$ab^2=ad\times bc$

so, this could be step to prove it

Seth is using the figure shown below to prove pythagorean theorem using triangle similarity: in the

answered: Guest

What is the inequality?

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