Justine wants to put a deck in the corner of her backyard in the shape of a right triangle. the length of one side of the deck is 7 feet more than the other side. the hypotenuse is 13. find the lengths of the two sides of the deck.

5

12

Step-by-step explanation:

Let x = length of a side of the deck

Let x - 7 = length of the other side.

Now let's use the Pythagorean Theorem.

a² + b² = c²

a = x

b = x+7

c = 13

Now that we have our values, let's plug them in.

x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

2x² + 14x + 49 = 169

Since it's a quadratic equation, we get 0 on one side.

2x² + 14x - 120 = 0

Now we factor out the greatest common factor

2(x²+7x-60) = 0

2(x + 12)(x - 5) = 0

Using the Zero product property, we get:

2 ≠ 0

x + 12 = 0

x = -12

x - 5 = 0

x = 5

Since x is a side of the triangle, x = -12 does not get included. So then we have:

x = 5

Now let's solve for the other side.

x + 7

5 + 7 = 12

Now that we have our value of x, let's put it in the formula to check.

x = 5

a² + b² = c²

x² + (x+7)² = 13²

5² + (5+7)² = 13²

25 + 144 = 169

169 = 169

the answer is 28

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.