Question

in triangle pqr pq equals 39 inches, pr equals 17 inches, and hte altitude pn equals 15 inches. find ar. consider all cases, two answers

Answer 1

`\text{The correct answer is QR is, 44 in.}`

Using Pythagoras theorem in ΔPNQ:

`\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PQ)^2=(PN)^2+(QN)^2}}`

• PQ = 39
• PN = 15

`\boxed{(39)^2=(15)^2+(QN)^2}\\\boxed{\bold{QN=√((39)^2-(15)^2) }}\\\boxed{QN=\bold{36}}`

`\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PR)^2=(PN)^2+(QN)^2}}`

• PR = 17
• PN = 15

`\boxed{\bold{(17)^2=(15)^2+(RN)^2}}\\\boxed{\bold{RN=√((17)^2-(15)^2) }}\\\boxed{RN=\bold{8}}}`

Adding the numbers:

36 + 8 = 44

`\text{Hence, The correct answer is QR is, 44 in.}`

Answer 2

In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 in.

How did we figure this out?

Solution:

`\boxed{\bold{= > (39)^2=(15)^2+(QN^2}}\\\boxed{= > QN=\bold{√((39)^2-(15)^2)} }\\\boxed{= > QN=\bold{36}}`

Now we have to determine the side RN.

• Side PR = 17

• Side PN = 15

Now put all the values in the above expression, we get the value of side RN.

`\boxed{\bold{= > (17)^2}=(15)^2+(RN)^2}\\\boxed{= > RN=\bold{√((17)^2-(15)^2) }}\\\boxed{= > RN=\bold{8}}`

• Side QR = 36 + 8

• Side QR = 44

Therefore, In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 inches.