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4 years ago

A cabinet door has a perimeter of 62 inches its area is 228 in.² what are the dimensions of the door

1 answer:

4 0

P=2(L+W)
A=LW

given
P=62
62=2(L+W)
divide 2
31=L+W
minus W
L=31-W

sub into other one
A=LW
A=(31-W)(W)
228=31W-W^2
times -1
W^2-31W=-228
add 228 both sides
W^2-31W+228=0
factor
what 2 numbers multiply to get 228 and add to get -31
-19 and -12
(W-19)(W-12)=0
set to zero

W-19=0
W=19

W-12=0
W=12

sub back

L=31-W
L=31-12
L=19
or
L=31-19
L=12

the doorway is 12in by 19in

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Find the area. The figure is not drawn to scale

poizon [28]

Answer:

96 square inches.

Step-by-step explanation:

From given picture we see that

BC=8 in

AD=10 in

Given that

AD=AB

Then AB=10 in

Apply Pythagorean theorem in triangle ABC to find AC

$(hypotenuse)^2=(base)^2+(perpendicular)^2$

$(AB)^2=(BC)^2+(AC)^2$

$(10)^2=(8)^2+(AC)^2$

$100=64+(AC)^2$

$100-64=(AC)^2$

$36=(AC)^2$

take square root

$6=AC$

Then area of triangle ABC $=\frac{1}{2}\left(base\right)\left(altitude\right)$

$=\frac{1}{2}\left(8\right)\left(6\right)=24$

There are total 4 congruent triangles.

Then total area of the given figure = 4(24)=96 square inches.

7 0

3 years ago

Solve the equation. Show your work. Check your answer.

Hitman42 [59]

4y+5=-31 you subtract 5 from both sides so you get 4y=-36 then you divide by 4 from both sides so you get y=-9 and to check you put -9 in for y and multiply 4 and -9 add 5 to get -31

6 0

3 years ago

A forest ranger can see for a distance of 12 miles from a firetower.How many square miles can he observe?

mr_godi [17]

I think it is 12x12 = 144

7 0

4 years ago

Damon is locked out of his house. The only open window is on the second floor. Which is 12 feet above the ground. He needs to bo

Sonja [21]

Use the Pythagorean theorem
A^2+b^2=c^2
12^2+5^2=c^2
144+25=c^2
169=c^2
13=c
13 foot ladder

6 0

3 years ago