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inna [77]
3 years ago
9

rhombus and a square have one and the same side of 6 cm. The area of the rhombus is 4/5 of the area of the square. Find the heig

ht of the rhombus.​
Mathematics
1 answer:
spin [16.1K]3 years ago
4 0

Answer:

1.8 is the <em>h</em> of the rhombus

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The area of the yellow region is 112 cm^2. find the value of x​
mrs_skeptik [129]
<h3>Answer:   x = 7</h3>

===========================================================

Explanation:

The largest rectangle (composed of the green and yellow sections combined) has area of 11*12 = 132 cm^2.

The yellow region takes up 112 of those 132 sq cm. This must mean the green region takes up 132-112 = 20 cm^2.

The horizontal portion of the green rectangle is 12-x cm. The vertical portion is 11-x cm. We can form the area of the green rectangle as an algebraic expression like so

area = length*width

area = (11-x)*(12-x)

area = 132 - 11x - 12x + x^2 .... apply the FOIL rule

area = x^2 - 23x + 132

Set this equal to the 20 cm^2 we found earlier.

x^2 - 23x + 132 = 20

x^2 - 23x + 132-20 = 0

x^2 - 23x + 112 = 0

We could factor or we could use the quadratic formula. I'll go with the second option.

We'll plug in a = 1, b =  -23, c = 112

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-23)\pm\sqrt{(-23)^2-4(1)(112)}}{2(1)}\\\\x = \frac{23\pm\sqrt{81}}{2}\\\\x = \frac{23\pm9}{2}\\\\x = \frac{23+9}{2}\ \text{ or } \ x = \frac{23-9}{2}\\\\x = \frac{32}{2}\ \text{ or } \ x = \frac{14}{2}\\\\x = 16\ \text{ or } \ x = 7\\\\

One of these solutions isn't feasible. Note how if x = 16, then this exceeds both the 11 cm and 12 cm sides. So this x value is not possible.

However, x = 7 is possible.

If x = 7, then the horizontal portion of the green rectangle is 12-x = 12-7 = 5 cm. Also, the vertical portion of the green rectangle would be 11-x = 11-7 = 4 cm. The area then is length*width = 5*4 = 20 cm^2 which matches up with what we got earlier. So the answer is confirmed.

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3 years ago
I need help finding the value of x so that all triangles have the same perimeter
Masteriza [31]
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3 years ago
Which algebraic expression represents the phrase "seven more than half of a number"?
Igoryamba

Answer:

i believe it is the first answer.

Step-by-step explanation:

3 0
3 years ago
to construct the midpoint of a segment, fold the paper so that the given line segment lies on itself and
Ludmilka [50]
And the endpoints lie on each other.
5 0
3 years ago
Read 2 more answers
Is this correct????? Please someone answer
Olegator [25]

Answer:

48 is right!!

Step-by-step explanation:

the pattern is +10 +9 +8 +7 +6 +5 and so on

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