The length of a rectangular painting is 3 inches longer than its width. if the diagonal is 15 inches long, what is the length of the painting? a. 9 inches b. 12 inches c. 13 inches d. 18 inches

ANSWER

12 inches

EXPLANATION

Let the length of the rectangular painting be inches, then the width will be inches.

Since the diagonal is the hypotenuse, we can apply the Pythagoras Theorem to find the length.

We expand to obtain;

We simplify to obtain a quadratic equation in .

We divide through by 2 to obtain.

We factor to obtain

Since we are dealing with length we discard the negative value.

Hence the length is 12 inches

B. 12 inches

Step-by-step explanation:

We know that the length of the rectangular painting is 3 inches longer than its width so we can write it as:

l = w + 3

and the diagonal is 15 inches long.

We can use use the Pythagoras Theorem to find the length of the painting.

(w)² + (w + 3)² = (15)²

w² + w² + 6w + 9 = 225

2w² + 6w - 216 = 0

w² + 3w - 108 = 0

(w + 12)(w - 9) = 0

w = -12 (ignore), w = 9  

So, l = w + 3

l = 12

Therefore, the length of the rectangle is 12 inches.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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