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3 years ago

The perimeter of a rectangle is 140 and the length is 10 more than four times the width. find the dimensions

Mathematics

2 answers:

aalyn [17]3 years ago

7 0

Answer:

Width = 12

Length = 58

Step-by-step explanation:

Width = x

Length = 4x + 10

Perimeter = 140

2 * ( length + width ) = 140

2 * (4x +10 + x) = 140

5x + 10 = 140/2 = 70

5x = 70- 10

5x = 60

x = 60/5 = 12

Width = 12

Length = 4 * 12 + 10 = 48 +10 = 58

aleksklad [387]3 years ago

7 0

Answer:

The dimensions of the rectangle is $58\times 12$ units.

Step-by-step explanation:

Given : The perimeter of a rectangle is 140 and the length is 10 more than four times the width.

To find : The dimensions ?

Solution :

Let the width of the rectangle is W=x

The length is 10 more than four times the width.

i.e. the length of the rectangle is L=4x+10

The perimeter of the rectangle is

$P=2(L+B)$

$140=2(4x+10+x)$

$70=5x+10$

$5x=60$

$x=\frac{60}{5}$

$x=12$

The width is 12 unit.

The length is 4(12)+10=48+10=58 unit.

Therefore, the dimensions of the rectangle is $58\times 12$ units.

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3 years ago

Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C'. Describe the transformation using words. Make s

tatyana61 [14]

Answer:

Part A

We note that the vertices of a triangle are formed by three non colinear points, which are A(3, 3), B(6, 6), C(9, 3)

The image of the reflection of a point (x, y) across the x-axis is (x, -y)

Therefore, the image of the triangle are; A'(3, -3), B'(6, -6), and C'(9, -3)

The characteristics of the transformation includes;

1) The dimensions of the preimage and image triangles are the same (rigid transformation)

2) The image is the representation of the inverted (upside down) of the preimage

3) The x-values of the image and the preimage are the same, while the y values are equal in magnitude but opposite in sign

Part B

Please find attached the drawing of the triangle ΔABC, ΔA'B'C' and the lines from A and and A' to the reflecting line, the x-axis

Based on the above characteristics, the perpendicular line drawn from A to the reflecting line(the x-axis and the line drawn from A' to the x-axis are equal in length and they intersect at the same point on the x-axis

Part C

Given that the x-axis values of B and B' and the magnitudes of the y-axis values of B and B' are the same, we have that the length of the perpendicular lines from B and B' will have equal length and point of intersection on the x-axis

Therefore, the same characteristics is seen when a line segment connecting B with the reflecting x-axis and then a line B' with the reflecting line is drawn

Step-by-step explanation: