All categories

2 years ago

1. The diagonal of a quadrilateral

Mathematics

1 answer:

zalisa [80]2 years ago

6 0

Consider the length of diagonal is 8.5 cm instead of 8.5 m because length of perpendiculars are in cm.

Given:

Length of the diagonal of a quadrilateral = 8.5 cm

Lengths of the perpendiculars dropped on it from the remaining opposite vertices are 3.5 cm and 4.5 cm.

To find:

The area of the quadrilateral.

Solution:

Diagonal divides the quadrilateral in 2 triangles. If diagonal is the base of both triangles then the lengths of the perpendiculars dropped on it from the remaining opposite vertices are heights of those triangles.

According to the question,

Triangle 1 : Base = 8.5 cm and Height = 3.5 cm

Triangle 2 : Base = 8.5 cm and Height = 4.5 cm

Area of a triangle is

$Area=\dfrac{1}{2}\times base \times height$

Using this formula, we get

$Area(\Delta 1)=\dfrac{1}{2}\times 8.5\times 3.5$

$Area(\Delta 1)=14.875$

and

$Area(\Delta 2)=\dfrac{1}{2}\times 8.5\times 4.5$

$Area(\Delta 2)=19.125$

Now, area of the quadrilateral is

$Area=Area(\Delta 1)+Area(\Delta 2)$

$Area=14.875+19.125$

$Area=34$

Therefore, the area of the quadrilateral is 34 cm².

You might be interested in

A textbook store sold a combined total of 294 physics and psychology textbooks in a week. The number of psychology textbooks sol

miv72 [106K]

Answer:

105 psychology textbooks. 189 physics textbooks.

5 0

3 years ago

A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is f

mestny [16]

Answer:

The value is $W= 2640 \ ft \cdot lb$

Step-by-step explanation:

From the question we are told that

The weight of the bucket is $F = 5 lb$

The depth of the well is $x_1 = 60 \ ft$

The weight of the water is $W_w = 42 lb$

The rate at which the bucket with water is pulled is $v = 1.5 \ ft/s$

The rate of the leak is $r = 0.15 lb/s$

Generally the workdone is mathematically represented as

$W = \int\limits^{x_1}_{x_o} {G(x)} \, dx$ ]

Here G(x) is a function defining the weight of the system (water and bucket ) and it is mathematically represented as

$G(x) = F + (W_w- Ix)$

Here I is the rate of water loss in lb/ft mathematically represented as

$I = \frac{r}{v}$

=> $I = \frac{0.15 }{1.5 }$

=> $I = 0.1$

$G(x) = 5 + (42- 0.1x)$

=> $G(x) = 47- 0.1x)$

$W = \int\limits^{60}_{0} {47- 0.1x} \, dx$ ]

=> $W = [47x - \frac{0.1x^2}{2} ]|\left 60} \atop {0}} \right.$

=> $W= [47(60) - 0.05(60)^2]$

=> $W= 2640 \ ft \cdot lb$

7 0

3 years ago

A the slope of f(x) is greater than the slope of g(x)

Komok [63]

To find the slope of g(x), use the slope formula(m):

$m=\frac{y_2-y_1}{x_2-x_1}$ And plug in two points, I will use:

(0, 2) = (x₁, y₁)

(5, 4) = (x₂, y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{4-2}{5-0}$

$m=\frac{2}{5}$

You could do the same to find f(x) by finding two points and using the slope formula, or you could use this to tell visibly:

$m=\frac{rise}{run}$

Rise is the number of units you go up(+) or down(-) from each distinguished point

Run is the number of units you go to the right from each distinguished point

If you look at the graph, you can see the points (0, -1) and (3, 1). From each point, you go up 2 units and to the right 3 units (you can make sure by using another point). So the slope of f(x) is $\frac{2}{3}$

Whichever line looks more vertical(and is positive) has the greater slope. So the slope of f(x) is greater than the slope of g(x). The answer is option A

7 0

3 years ago

If 8 cakes cost £4.00 how much would 3 cakes cost?

zzz [600]

Hello!

To calculate how much 3 cakes would cost, we must first find the cost of each individual cake.

To do this, we must divide the cost of 8 cakes by 8 cakes.

4.00 ÷ 8 = 0.5

This means that each individual cake costs $0.50. Multiply this by 3 to find the cost of 3 cakes.

0.50 × 3 = 1.50

Therefore, 3 cakes would cost $1.50.

4 0

3 years ago

Read 2 more answers

What is the value of n

Trava [24]

Answer:

c. 38

Step-by-step explanation:

5 0

3 years ago