All categories

2 years ago

Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is the other diagonal?

Mathematics

1 answer:

inn [45]2 years ago

7 0

Answer:

70 units.

Step-by-step explanation:

The 4 sides of a rhombus are equal so each side has length 148 /4

= 37 units. The diagonals bisect each other at right angles so when we draw the 2 diagonals we have 4 congruent right-angled triangles.

So consider one of these triangles:

The hypotenuse is 37 units and one of the legs = 1/2 * 24 = 12 units ( half of the diagonal of length 24).

So the other leg is found using Pythagoras:

x^2 = 37^2 - 12^2 = 1225

x = 35.

This is half of the other diagonal so the latter = 70 units.

You might be interested in

Find the value of t in the diagram

12345 [234]

In a trapezoid, with bases $b$ and $B$ and height $h$ , the area is given by

$A = \frac{(B+b)h}{2}$

In your case:

$B = BC = 3t$

$b = AD = t$

$h = AB = t$

so, the formula becomes

$A = \frac{(3t+t)t}{2} = \frac{4t^2}{2} = 2t^2$

Since the area is $50 \text{cm}^2$ , we have

$2t^2 = 50 \iff t^2 = 25 \iff t = 5$

5 0

2 years ago

Read 2 more answers

I NEED HELP THIS IS DUE IN 15 mins PLSSS SOMEBODY HELP ME!!!!!

Lera25 [3.4K]

Answer:

$Standard \: form :\:y= {x}^{2} - 4x - 5\\Factored\: from:\:y = (x + 1) (x - 5)$

Step-by-step explanation:

$y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form$

8 0

2 years ago

8. Solve the system using substitution. Show all work. (3 points)

Minchanka [31]

Ok. first you have to pick x or y or whatever variable you have and the number multiplied with it has to be the same in each equation but one has to be positive and one negative.
lets pick x

y=-2x+6
3y=x-3/ *2

so the x are positive and negative we have to multiply the equation with 2

y=-2x+6
6y=2x-6

now you have to add the equations. you do that by adding each side of the equatins together like this:

y+6y=-2x+6+2x-6 the x will cancel out

7y=0
y=0

now just go back to one of the previous equations and put the y in it.

0=-2x+6
2x=6
x=3

here you go

3 0

2 years ago

PLEASE HELP IF I DONT GET THIS IN 10 MIN ILL BE TOAST

Nikolay [14]

Answer:

your answer will be

1 -y is a variable

3- y is a term

4 -9 is a constant

6- 9 is a term

Step-by-step explanation:

if i'm wrong please correct me i hope i helped though

6 0

1 year ago

Give the rate in miles per hour. Round to the nearest tenth.

miv72 [106K]

Answer:

51.8mph

Side note: Caroline isn't human. Walking almost 52 miles per hour is humanly impossible

Hope I helped! ☺

4 0

2 years ago