*The rectangle has a perimeter of 38 meters.

Mathematics

1 answer:

Scilla [17]3 years ago

8 0

Answer:

Width of the rectangle = 7 meters

Length of the rectangle = 12 meters

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Perimeter of the rectangle = 38 meters

Width of the rectangle = w

Length of the rectangle = w + 5

Perimeter of a rectangle = 2(length + width)

38 = 2{(w + 5) + w}

38 = 2(w + 5 + w)

38 = 2(2w + 5)

38 = 4w + 10

38 - 10 = 4w

28 = 4w

w = 28/4

w = 7 meters

Width of the rectangle = w

= 7 meters

Length of the rectangle = w + 5

= 7 + 5

= 12 meters

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Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*

Veronika [31]

Answer:

The area of the triangle DEF is 10.

Step-by-step explanation:

Area of a Triangle:

A triangle of base B and height H (both must be perpendicular) has an area of:

$\displaystyle A=\frac{BH}{2}$

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

$\displaystyle A=\frac{5*4}{2}=10$