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melisa1 [442]
3 years ago
8

One side of a right triangle is 2 cm shorter than the hypotenuse and 7 cm longer than the third side. find the lengths of the si

des of the triangle.
Mathematics
1 answer:
astra-53 [7]3 years ago
8 0
The right angles triangle has three sides including the hypotenuse which is opposite to the right angle.
If the hypotenuse - H
Then one side is - H - 2
Third side is 7 cm shorter then H-2
Therefore it’s H -2-7 = H -9
According to Pythagoras theorem
Square of hypotenuse = sum of the squares of the other 2 sides
H² = (H-9)² + (H-2)²
H² = H² -18H + 81 + H² -4H + 4
0 =H² -22H +85
This is a quadratic equation
0 = H² - 17H -5H +85
0 = H (H - 17) -5(H-17)
(H-17) (H-5) =0
H -17=0 or H-5=0
H could be 17 cm or 5 cm
If H =5 cm then
Side 1 -H-2 = 3 cm
And side 2 - H-9 = -4 cm
Since lengths cannot be negative values
H isn’t 5 cm
Therefore H =17 cm
1 side is H-2 = 15 cm
2nd side H -9 = 8 cm
Three sides are 17 cm, 15 cm and 8 cm
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The answer to all of these word problem
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Answer:Hope this helps!

Number 1 = 2   and 1/8

Number 2 = 6   and 3/40

Number 5 = 4    and 2/6

Number 6 = 15 and 1/3


Step-by-step explanation:


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Island Rent-a-Car charges a car rental fee of $40 plus $5 per hour. Wayne's Wheels charges a car rental fee of $25 plus $7.50 pe
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Step-by-step explanation:

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3 years ago
Sally and Karl work at different jobs. Sally earns $7 per hour and Karl earns $5 per hour. They each earn the same amount per we
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Answer:

Karl works 7 hours a week

Step-by-step explanation:

Step 1: Determine total amount that Sally earns

Total amount Sally earns=rate per hour×number of hours worked(h)

where;

Rate per hour=$7 per hour

Number of hours worked=h

Replacing;

Total amount Sally earns=(7×h)=7 h

Step 2: Determine total amount Karl earns

Total amount Karl earns=rate per hour×number of hours worked

where;

rate per hour=$5

number of hours worked=2 more than Sally=h+2

replacing;

Total amount Karl earns=5(h+2)

Step 3: Equate Sally's total earnings to Karl's total earnings and solve for h

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7 h-5 h=10

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Karl works (h+2) hours=(5+2)= 7 hours

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7 0
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