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dezoksy [38]
3 years ago
14

If the perimeter of a right triangle is 42 units and the length of the hypotenuse is 20 units, find the length of the other two

sides of the triangle.
Can you please show work
Mathematics
1 answer:
Mashutka [201]3 years ago
4 0
So
a^2+b^2=c^2
c=hypotenuse
a^2+b^2=20^2=400

if the permiter is 42 then
p=hypotonuse+side+side
42=20+side+side
subtract 20 from both sides
22=side+side

a+b=22
subtract b from both sides
a=22-b
subsitute for a in equation below
a+2+b^2=c^2
(22-b)^2+b^2=400
b^2-44x+484+b^2=400
2b^2-44x+484=400
divide both sides by 2
b^2-22x+242=200
subtract 200 from both sides
b^2-22x+42=0
factor
(b+/-number)(b+/-number)
to find the numbers, find which 2 number multiply to 42 and add to get -22
the numbers must be neative since same signs multiplied=positive and negative+negative=negative
(b-number)(b-number)
facrors of 42=2,3,6,7,14,21
2,21
3,14
6,7
it's hard to find the number, but the numbers are -19.8882 and -2.11181
(b-19.8882)(b-2.11181)=0
if xy=0 then assume that x and y=0

b-19.8882=0
add 19.8882 to both sides
b=19.8882

b-2.11181=0
add 2.11181 to both sides
b=2.11181



the side legnths are 19.8882 units and 2.11181 units
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Taylor runs a smoothie shop and is in placing his order for a week.Each week he needs to have 2 gallons of pineapple juice and 4
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Answer:

For pineapple juice

He need 160 more ounces of pineapple juice.

For orange juice

He needs 352 ounces more of orange juice.

Step-by-step explanation:

1 liquid gallon = 4 liquid quarts

1 liquid quart = 32 fluid ounces

Taylor runs a smoothie shop and is in placing his order for a week.

We are told that:

Each week he needs to have

a) For pineapple juice

2 gallons of pineapple juice

We convert these to quarts and ounces

1 gallons = 4 quarts

2 gallons = 2 × 4

= 8 quarts of pineapple juice

If he already has 3 quarts of pineapple juice

She needs: 8 quarts - 3 quarts

= 5 quarts

Converting these to ounces

1 liquid quart = 32 fluid ounces

5 quarts = x

Cross Multiply

=5 × 32 fluid ounces

= 160 fluid ounces

2) For orange juice

She needs to have 4 gallons of orange juice on hand

We convert these to quarts and ounces

1 gallons = 4 quarts

4 gallons = 4 × 4

=Hence she needs to have: 16 quarts of pineapple juice

If he already has 5 quarts of orange juice

She needs: 16 quarts - 5 quarts

= 11 quarts more

Converting these to ounces

1 liquid quart = 32 fluid ounces

11 quarts = x

Cross Multiply

=11 × 32 fluid ounces

= 352 fluid ounces

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3 years ago
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