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Korolek [52]
3 years ago
5

The first floor of a house consists of a kitchen And dining room. The areas of the living room ,kitchen, and dining room are in

the ratio of 3:2:1. The combined area of all three rooms is 576 square feet.
A. What is the area of the dining room?
B. What is the area of the kitchen?
C. What is the area of the living room?
Mathematics
1 answer:
Stella [2.4K]3 years ago
4 0

Answer:

A: 96 B:192 C:288

Step-by-step explanation:

3+2+1=6

Divide 576 by 6 to get 1/6, you will get 96.

so 96 is the area of the dining room.

Multiply 2 times 96, since that would be 2/6.

That would be 192.

So 192 would be the area of the kitchen.

Here's a trick: all you need to do is add 96 and 192 now (or multiply 96 by 3), because that is half of the areas, 3/6.

So 96 times 3 is 288.

The living room is 288.

To check our work, we can add 288 by 96 by 192.

We would end up with 576, which was our original number.

So 288:192:96.

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Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try
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Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

P=2(L+W)

where

L is the length of rectangle

W is the width of rectangle

we have

F(-2,5),R(-2,1),O(6,1),G(6,5)

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

so

FG=RO=L\\RF=OG=W

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find the distance FG

F(-2,5),G(6,5)

substitute the values

d=\sqrt{(5-5)^{2}+(6+2)^{2}}

d=\sqrt{(0)^{2}+(8)^{2}}

FG=8\ units

step 2

Find the distance RF

R(-2,1),F(-2,5)

substitute the values

d=\sqrt{(5-1)^{2}+(-2+2)^{2}}

d=\sqrt{(4)^{2}+(0)^{2}}

RF=4\ units

step 3

Find the perimeter

P=2(L+W)

we have

FG=RO=L=8\ units\\RF=OG=W=4\ units

substitute

P=2(8+4)=24\ units

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

A=LW

we have

FG=RO=L=8\ units\\RF=OG=W=4\ units

substitute

A=(8)(4)=32\ units^2

8 0
3 years ago
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