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1 year ago

TASK 3

Mathematics

1 answer:

Fofino [41]1 year ago

8 0

The area will be equal to Area = (28)(21) / 2 = 294 square inches.

To determine the area of a triangle, we calculate one half of the product of the base and the height of the triangle so we need data on its base and its height. We are given the following:

Hypotenuse = 7 + base = 14 + height

Perimeter = 84 inches

The perimeter of the triangle is equal to the sum of the three sides of the triangle which are the height, base and hypotenuse. So,

Perimeter = height + base + hypotenuse = 84

We let x = height and y = base. We calculate area as follows:

84 = x + y + (7 + y)

77 = x + 2y

x = 77 -2y

The Hypotenuse is related to the other sides by the Pythagorean theorem.

Hypotenuse^2 = (x^2 + y^2)

(14 + x)^2 = x^2 + y^2

(14 + (77-2y))^2 = (77-2y)^2 + y^2

(91-2y)^2 = (77-2y)^2 + y^2

Solving for y and x

y = 28

x = 21

Area = (28)(21) / 2 = 294 square inches

To know more about the area follow

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2 years ago

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3 years ago

Henry had 20 convertibles and 5 trucks in his miniature car collection. After Henry's aunt bought him some more miniature trucks

saw5 [17]

Answer:

Her aunt buy 75 trucks.

Step-by-step explanation:

Given:

Henry had 20 convertibles and 5 trucks in his miniature car collection. After Henry's aunt bought him some more miniature trucks, Henry noticed that a fifth of his collection were convertible.

Now, to find the trucks her aunt buy.

Let the total collection of Henry be $x.$

Number of trucks Henry had in his collection = 5.

Number of convertibles Henry had in his collection = 20.

As, Henry's $\frac{1}{5}$ collection were convertible.

Now, to get the total number of collection:

$\frac{1}{5}\ of\ x=20.$

$\frac{1}{5} \times x=20$

Multiplying both sides by 20 we get:

$x=100.$

Total collection of Henry = 100.

So, the total number of trucks he had in his collection is:

Total collection of Henry - number of convertibles Henry had in his collection.

$=100-20$

$=80.$

Hence, Henry had total 80 trucks in his collection.

And 5 trucks he had already in his miniature car collection.

Now, to get the number of trucks her aunt buy we subtract trucks he had already in his miniature car collection from the total number of trucks in Henry's collection:

Total number of trucks in Henry's collection - Number of trucks already in his miniature car collection.

$=80-5$

$=75.$

Therefore, her aunt buy 75 trucks.

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3 years ago