All categories

3 years ago

The perimeter of the right angle triangle is 96cm

2 answers:

7 0

Given : the perimeter of the right angle triangle is 96cm the length in sides are in a ratio 6:8:10. work out the area of the triangle in cm²

Need to Find : The area of the Rectangle

_____________________________________

Let us assume the constant multiple be x

So,

Let the length be 10x

Let the breadth be 6x

Let the height be 8x

Now, as we know that the Perimeter of rectangle is 96 cm

★ Perimeter = Sum of all three sides of a triangle

➛ 96 cm = 6x + 8x + 10x

➛ 96 cm = 24x

➛ x = 96/24

➛ x = 4 cm

Putting x = 4 we get

Length = 10(4) = 40 cm

Breadth = 6(4) = 24 cm

Height = 10(4) = 32 cm

As we know that

★ Area = ½ × Base × Height

➛ Area = ½ × 24 × 32

➛ Area = 12 × 32

➛ Area = 384 cm²

Henceforth the area is 384 cm²

Bess [88]3 years ago

3 0

Answer:

384 cm^2

Step-by-step explanation:

The perimeter is calculated by adding all side lengths

if the ratio is 6:8:10 then let x represent the numbers

then we can make this equation

6x + 8x + 10x = 96

24x = 96 divide both sides by 24

x = 4 the side lengths are 6*4, 8*4 and 10*4

The area of a triangle is calculated by multiplying height and base and that divided by two

in right triangles the height is the larger leg and the base is the shorter leg

so the area of this triangle is :

32*24 / 2 = 384 cm^2

You might be interested in

A solid object is made up of two cubes resting side by side. One cube has an edge length of 5.3 ft, and the other cube has an ed

Debora [2.8K]

Answer:

2.8

Step-by-step explanation:

3 0

3 years ago

IS (1,-4) a solution to the equation y=-2?

matrenka [14]

Answer:

yes

Step-by-step explanation:

7 0

2 years ago

On the map the scale is 1 inch=125 miles. What is the actual distance between the two cities if the map distance is 2 3/4 inches

ss7ja [257]

291.6 or rounded 292 miles

7 0

3 years ago

Read 2 more answers

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

A person invests $1,150 in an account that earns 5% annual interest compounded continuously. Find when the value of the investme

AfilCa [17]

Answer:

11.1 years

Step-by-step explanation:

The formula for interest compounding continuously is:

$A(t)=Pe^{rt}$

Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:

$2000=1150e^{{.05t}$

We will simplify this first a bit by dividing 2000 by 1150 to get

$1.739130435=e^{.05t}$

To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with

ln(1.739130435)=.05t

Taking the natural log of that decimal on our calculator gives us

.5533852383=.05t

Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.

7 0

2 years ago