All categories

3 years ago

The perimeter of the rectangle is 76 units. Find the length of side pq

Mathematics

1 answer:

larisa [96]3 years ago

6 0

Answer: $PQ=16\ units$

Step-by-step explanation:

The missing figure is attached.

The perimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

You can identify in the figure that:

$w=SR=PQ=2z+2\\\\l=QR=PS=3z+1$

Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:

$76=2(3z+1)+2(2z+2)$

Now you must simplify and solve for "z"

$76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7$

Finally, substituting the value of "z" into $PQ=2z+2$ , you get:

$PQ=2(7)+2=16\ units$

You might be interested in

Fifty people enter a contest in which three identical prizes will be awarded. in how many different ways can the prizes be award

Nina [5.8K]

<span>Provided that no one can receive more than one prize, there are 50*49*48= 117600 ways to distribute the prizes. The first prize can be given to any of the 50 people, the second to any of the remaining 49, and the third to the remaining of the 48, multiplying these possibilities together leads to the answer.</span>

4 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through the points (4,-9) and ? (8,-3) Write your answer in simplest form.

Mariana [72]

The slope of the line =1.5x - 15

8 0

3 years ago

Read 2 more answers

What is the solution for the equation 5/3b^3-2b-5=2/b3-2

irinina [24]

Answer:

Option C is correct.

Step-by-step explanation:

Given Equation:

$\frac{5}{3b^3-2b^2-5}=\frac{2}{b^3-2}$

To find: Solution of the Equation.

Consider,

$5(b^3-2)=2(3b^3-2b^2-5)$

$5b^3-10=6b^3-4b^2-10$

$6b^3-5b^3-4b^2+10-10=0$

$b^3-4b^2=0$

$b^2(b-4)=0$

b² = 0 ⇒ b = 0

b - 4 = 0 ⇒ b = 4

Therefore, Option C is correct.

7 0

3 years ago

Read 2 more answers

The legs of a right triangle are 5 and 7 cm long, respectively. What is the length of the hypotenuse? If necessary, round your a

valentinak56 [21]

A squared plus B squared equals C squared, so what you need to do it square 5 and 7. 5 = 25 7 = 48 Then add then and square root your answer. 48 + 25 = 73. 73 square rooted equals an rounded amount of 8.6. SO the answer is D

4 0

3 years ago

Look at the image below plz correct answers Surface area of cones 15 points

monitta

Answer:

$A\approx 282.7\ m^2$

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is to use the Pythagorean theorem to find the height of the cone. Then one can substitute the values given and found on the cone into the formula to find the surface area in order to solve for the surface area of the given cone.

2. Height of the cone

Imagine drawing a line from the tip of the cone down to the center of the base. This line will form a right angle with the base, thus, a right triangle is formed between the line, the radius (the distance from the center to the circumference or outer edge on a circle) of the base, and the incline of the cone. The Pythagorean theorem is a formula that relates the sides of a right triangle. This formula is as follows:

$a^2+b^2=c^2$

Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle, and (c) is the hypotenuse or the side opposite the right angle of the right triangle. Substitute the given values into the formula and solve for the unknown, or rather the height of the cone:

$a^2+b^2=c^2$

$a^2+5^2=13^2$

Simplify,

$a^2+5^2=13^2$

$a^2+25=169$

Inverse operations,

$a^2+25=169$

$a^2=144$

$a=12$

$h=12$

3. Find the surface area of the cone.

The following formula can be used to find the surface area of a cone:

$A=\pi r(r+\sqrt{h^2+r^2})$

Where ( $\pi$ ) represents the numerical value (3.1415...), (r) represents the radius of the base, and (h) represents the height of the cone. Substitute the given values into the formula and solve for the surface area: