The perimeter of a rectangle is 136 ft. The ratio of its length to its width is 9:8. What are the dimensions of the rectangle?

Mathematics

2 answers:

mestny [16]3 years ago

5 0

B) 44 ft by 24 ft..........:.

KATRIN_1 [288]3 years ago

4 0

2100000000000000000000000000000000000000000000000000000000000000000

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Geometry help! Please prove the following is a square with full explanation, I'm really lost.

Hoochie [10]

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope. We don't have to bother to take the square root. We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6). slope=-6/-1=6 AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1). slope=1/-6=-1/6. BC²=(-6)²+1²

CD=D-C=(1, 6). slope=6/1=6 CD²=1²+6²=37

DA=A-D=(6,-1) slope=-1/6 DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides. We see they all have squared distance 37. Equal perpendicular sides proves its a square.

If we do these problems enough we learn: There's no point taking the square root. In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides: (-1, -6) (-6, 1) (1, 6) (6,-1)

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Mrac [35]

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the answer is C.

Step-by-step explanation:

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Which graph represents the function f(x)= -2^x - 1

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the first graph does////=//

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3 years ago

A student solved the following problem and made an error: Triangles ABC and DEF. Angles A and F are congruent and measure 135 de

dmitriy555 [2]

We have that
triangle ABC coordinates
A (0,2) B(2,4) C(0,0)

triangle DEF coordinates
D (2,0) E ( 4,4) F (4,2)

using a graph tool
see the attached figure

therefore

Line 1 Segment AC equals 2. Segment FE equals 2. Segment AC is congruent to segment FE
so
Segment AC equals 2-------> is correct
Segment FE equals 2-----> is correct
Segment AC is congruent to segment FE------> is correct

Line 2 ∠A ≅ ∠F------> is correct

Line 3 Length of segment AB. A (0, 2) B (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment AB = 2.83

find the distance AB
d=√[(4-2)²+(2-0)²]--------> d=√[4+4]-----> d=√8-----> d=2.83
AB=2.83
so
Line 3 is correct

Line 4 Length of segment DE. D (2, 0) E (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment DE = 4.47

find the distance DE
d=√[(4-0)²+(4-2)²]--------> d=√[16+4]-----> d=√20-----> d=4.47
DE=4.47
so
Line 4------> is correct

Line 5 segment AB is congruent with segment DE
AB is not congruent with DE
so
Line 5 is not correct

therefore

the answer is
the student make the first mistake in line 5

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4 years ago