Mathematics, 20.10.2020 14:01 amandafutch24

19th October, 2020 the diagram below is a plane figure made up
of a rectangle of sizes 50m by 28 m and an
equilateral of height 24 cm. A circle is cut-out
of the rectangle as shown. If the circle
touches the three sides of the rectangle Calculate
a) the perimeter of the figure
the remaining portion of the figure.

19th October, 2020

the diagram below is a plane figure made upof a rectangle of sizes 50m by 28 m

Answers: 1

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Answers

Answer from: taseem001

Step-by-step explanation:

Equilateral Triangle:

Side of triangle = breadth of rectangle

= 28 cm

height = 24 cm

Area of triangle = $\frac{1}{2}base * height\\\\$

= $\frac{1}{2}*28*24$

= 28* 12

= 336 square cm

Rectangle:

length = 50 m

breadth = 28 m

Area of rectangle = length * breadth

= 28 * 50

= 1400 square cm

Diameter of circle = breadth of rectangle

d = 28 cm

r = 28/2 = 14 cm

Area of circle = πr²

$= \frac{22}{7}*14*14\\\\= 22 * 2 * 14$

= 616 square cm

Area of the remaining portion = Area of rectangle - area of circle + area of triangle

= 1400 - 616 + 336

= 1120 square cm

Perimeter of the figure = 28 + 50 + 28 + 28 + 50

= 184 cm

Hint: Perimeter of the figure. three side of rectangle + two sides of triangle

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

Th is not an attachment

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