All categories

3 years ago

The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.

Mathematics

2 answers:

aalyn [17]3 years ago

8 0

Answer:

length = 15 cm

Width = 12 cm

Step-by-step explanation:

Let width = w cm

Length = w + 3

Perimeter of rectangle = 54 cm

2 * (length + width) = 54

2 * (w+3 + w) = 54 {Add like terms}

2 *(2w + 3) = 54

2*2w + 2 * 3 = 54

4w + 6 = 54

Subtract 6 form both sides

4w = 54 - 6

4w = 48

Divide both sides by 4

w = 48/4

w = 12 cm

Length = 12 + 3= 15 cm

Anuta_ua [19.1K]3 years ago

3 0

Answer:

Length = 15cm

Step-by-step explanation:

let width be x

length = x+3

Perimeter = 2(l + b)

Perimeter = 54cm

equating:

2(x + x + 3) = 54

2(2x +3) = 54

4x + 6 = 54

4x = 54 - 6

4x = 48

x = 48/4 = 12

width = x = 12cm

length = x +3 = 12 + 3 = 15cm

You might be interested in

The Blair family was one of the first to come to the original 13 colonies (now part of the USA). They had 4 children. Assuming t

Mumz [18]

Answer:

31.25% probability that the Blair family had at least 3 girls

Step-by-step explanation:

For each children, there are only two possible outcomes. Either it was a girl, or it was not. The probability of a child being a girl is independent of any other children. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

They had 4 children.

This means that $n = 4$

The probability of a child being a girl is 0.5

This means that $p = 0.5$

Probability of at least 3 children:

$P(X \geq 3) = P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{4,3}.(0.5)^{3}.(0.5)^{1} = 0.25$

$P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625$

$P(X \geq 3) = P(X = 3) + P(X = 4) = 0.25 + 0.0625 = 0.3125$

31.25% probability that the Blair family had at least 3 girls

3 0

3 years ago

The measure of one angle of an octagon is two times smaller that of the other seven angles. What is the measure of each angle?

Anestetic [448]

Answer:

7 of the angles measure 144 degrees each and one angle measures 72 degrees

Step-by-step explanation:

Let

x -----> represent the measures of the seven same-size angles,

x/2 ----> represent the measure of the one that is "two times smaller."

we know that

The sum of internal angles of a polygon can be calculated as:

$S=180^o(n-2)$

where

n is the number of sides of the polygon

In this case

n=8 (octagon)

substitute

$S=180^o(8-2)=1,080^o$

The linear equation that represent this problem is

$\frac{x}{2}+7x=1,080$

solve for x

$\frac{15x}{2}=1,080\\\\15x=2,160\\\\x=144^o$

$\frac{x}{2}=72^o$

therefore

7 of the angles measure 144 degrees each and one angle measures 72 degrees

7 0

2 years ago

Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these

ANEK [815]

Answer:

The correct option is;

∠A ≅ ∠X

Step-by-step explanation:

The given coordinates of the points of triangle ACB are;

A(-4, 4), C(-1, 3), B(-4, 0)

The given coordinates of the points of triangle XYZ are;

X(0, 8), Y(8, 8), Z(6, 2), therefore, we have

The length. l. of segment is given by the following formula;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

For the length of the segment AC; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-1, 3), l = √(10)

For the length of the segment AB; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-4, 0), l = 4

For the length of the segment BC; (x₁, y₁) = (-4, 0), (x₂, y₂) = (-1, 3), l = 3·√2

For the length of the segment XY; (x₁, y₁) = (0, 8), (x₂, y₂) = (8, 8), l = 8

For the length of the segment XZ; (x₁, y₁) = (0, 8), (x₂, y₂) = (6, 2), l = 6·√2

For the length of the segment ZY; (x₁, y₁) = (6, 2), (x₂, y₂) = (8, 8), l = 2·√(10

Therefore;

XY ~ AB, XZ ~ BC, ZY ~ AC

Which gives;

∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z

8 0

3 years ago

Read 2 more answers

What’s the shade to this problem!? PLZ HELP I REALLY NEED THIS HELP!!!

Mashcka [7]

Answer:

the bottom section

Step-by-step explanation:

cause

6 0

3 years ago

It took Jaheim 2 hours to read the first 100 pages of a book what was his speed?

jeka94

If in 2 hours he read 200 pgs then in 1 hour will be 50 pgs

4 0

3 years ago

Read 2 more answers

The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.​

The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.