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steposvetlana [31]
2 years ago
12

The length of a rectangle is 4 m more than the width. If the area of the rectangle is 77 m2. How many meters long is the width o

f the rectangle?
Mathematics
1 answer:
kenny6666 [7]2 years ago
7 0

Step-by-step explanation:

length = width + 4

length×width = 77

using the first in the second equation

(width + 4)×width = 77

width² + 4width = 77

now, what square or squaring factors can create this ?

we are looking for (width + a)(width + b).

we know, this is

width² + (a+b)width + ab

so, what a, b can create 4 (the factor in our actual equation) ?

1, 3 and 2, 2, if we are only looking at whole numbers.

and which of the possibilities can we use to turn 77 into a square number ?

81 is only 4 away ...

2+2 = 4.

aha !

so, we can actually say our equation is

width² + 4width + 4 = 77 + 4

and then

(width + 2)² = 81

width + 2 = 9

width = 7 m

length = width + 4 = 7 + 4 = 11 m

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Read 2 more answers
the diameter of a piston for an automobile is 3 11/16in with tolerence of 1/64in. find the upper and lower limits of the pistons
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Upper Tolerance

Remark

The 11/16 is the only thing that will be affected. The three won't go up or down when we add 1/64 so we should just work with the 11/16. We need only add 11/16 and 1/64 together to see what the upper range is. Later on we can add 3 into the mix.

Solution

<u>Upper Limit</u>

\dfrac{11}{16} +  \dfrac{1}{64}

Now change the 11/16 into 64. Multiply numerator and denominator or 11/16 by 4

\dfrac{11*4}{16*4} +  \dfrac{1}{64}

\dfrac{11*4}{16*4} +  \dfrac{1}{64} Which results in

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With a final result for the fractions of 45/64

So the upper tolerance = 3 45/64

<u>Lower Tolerance</u>

Just follow the same steps as you did for the upper tolerance except you subtract 1/64 like this.

\dfrac{11}{16} - \dfrac{1}{64}

Your answer should be 3 and 43/64


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