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amid [387]
1 year ago
14

A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti

on. Round your answer to the nearest hundredth of a centimeter.
Mathematics
1 answer:
yawa3891 [41]1 year ago
8 0

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have  b=\frac{42}{h}. Then, you can replace it in equation 1.

2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0

Now, you should solve the quadratic equation.

h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}

h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}

h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm

h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm

If h1=9.65 cm, then b_1=\frac{42}{9.65} =4.35 cm, and if  h2=4.35 cm, then b_1=\frac{42}{4.35} =9.65 cm.

Read more about the quadratic function here:

brainly.com/question/1497716

#SPJ1

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snow_tiger [21]

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$8.75 is your answer.

Step-by-step explanation:

What you do is you multiply 1.25 by 7.

<em>1.25 x 7 = $8.75</em>

$8.75 is your answer.

4 0
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4 a + 5 b when a = 4 and b = - 1.2
Firdavs [7]

The answer is 10.

4 a + 5 b when a = 4 and b = - 1.2

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Cylinder height of 7 and a radius of 4 cm. How many cubic centimeters of fluid can fill this cylinder
Alex Ar [27]

Answer:

112π = 351.86 cubic centimeters of fluid to fill the cylinder

Step-by-step explanation:

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4 0
2 years ago
A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real num
yKpoI14uk [10]

Answer: hypotenuse = c^{2} + b^{2}

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side (s_{1},s_{2}) of the right triangle, .i.e.:

h^{2} = s_{1}^{2} + s_{2}^{2}

In this question:

s_{1} = c^{2}-b^{2}

s_{2} = 2bc

Substituing and taking square root to find hypotenuse:

h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}

Calculating:

h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}

h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}

c^{4}+b^{4}+2b^{2}c^{2} = (c^{2}+b^{2})^{2}, then:

h=\sqrt{(c^{2}+b^{2})^{2}}

h=(c^{2}+b^{2})

Hypotenuse for the right-angled triangle is h=(c^{2}+b^{2}) units

3 0
3 years ago
Is the figure a rectangle? Explain.
luda_lava [24]

The correct option is b. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

<h3>How to explain the information?</h3>

The figure is a parallelogram and one diagonal measure 28 units.

In this case, it is not a rectangle because the sides of the parallelogram do not meet at right angles.

Therefore, the correct option is B.

Learn more about rectangles on:

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5 0
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