Mathematics, 17.02.2021 14:10 esme72

PLS ANSWER WILL GIVE 10 PTS The perimeter of a parallelogram is 164 cm. The diagonals intersect one another at 90°. One diagonal is bisected into segments of lengths 1500/x + 10 and x − 10 cm. Determine the length of the shorter diagonal.

a) 50 cm
b) 18 cm
c) 41 cm
d) 9 cm

Answers: 3

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Answer from: AriyaSeifert

b) 18 cm

Work Shown:

Since the parallelogram has perpendicular diagonals, this means that we're dealing with a rhombus. A rhombus has all four sides equal to one another.

One diagonal is bisected, or cut in half, to form the smaller pieces of length (150/x) + 10 and x-10. Set these two expressions equal to each other and solve for x

(150/x) + 10 = x-10

1500/x = x-10-10

1500/x = x-20

1500 = x(x-20)

1500 = x^2-20x

0 = x^2-20x-1500

x^2-20x-1500 = 0

(x-50)(x+30) = 0

x-50 = 0 or x+30 = 0

x = 50 or x = -30

We'll ignore the negative x value as it leads to a negative length which doesn't make sense.

If x = 50, then

x-10 = 50-10 = 40 (150/x)+10 = (150/50)+10 = 30+10 = 40

Each piece of this diagonal is 40 cm long.

The two smaller pieces combine to 40+40 = 80, which is the length of one of the diagonals. If this was the shorter diagonal, then 80 would be listed as part of the answer choices. However, 80 is not one of the answers.

Note how the two diagonals of the rhombus cut the figure into four right triangles.

Each right triangle has one known leg to be 40 and an unknown leg of y. The hypotenuse is 164/4 = 41 since we divide the perimeter by the four equal sides of the rhombus.

We'll use the pythagorean theorem to find the value of y

a^2 + b^2 = c^2

40^2 + y^2 = 41^2

1600 + y^2 = 1681

y^2 = 1681-1600

y^2 = 81

y = sqrt(81)

y = 9

This represents half of the other diagonal, so the full length of this other diagonal is 2*9 = 18 cm.

Answer from: bella2284

b) 18 cm

Step-by-step explanation:

happy to help ya :)

Answer from: Quest

step-by-step explanation: a reaction is first order. if the initial reactant concentration is 0.0200 m, and 25.0 days later the concentration is 6.25 x 10-4 m, then its half-life is:

Answer from: Quest

$\dfrac{p}{4}$ or $\dfrac{1}{4}p$

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is $\dfrac{p}{4}$ or $\dfrac{1}{4}p$

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PLS ANSWER WILL GIVE 10 PTS The perimeter of a parallelogram is 164 cm. The diagonals intersect one...

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