The length of QR is 44 inches
Step-by-step explanation:
In Δ PQR
- PQ = 39 inches
- PR = 17 inches
- PN is the altitude of it and its length is 15 inches
We need to find QR
To solve this problem we will use Pythagoras Theorem let us revise it
In ΔABC, if b is the right angle, then AC is called the hypotenuse of the Δ, AB , BC are its two legs, the relation between them is:
(AC)² = (AB)² + (BC)²
In Δ PQR
∵ PN is the altitude
∴ PN ⊥ QR
∴ m∠PNQ = m∠PNR = 90°
In ΔPNQ
∵ m∠PNQ = 90° ⇒ proved
- PQ is the hypotenuse
∴ (PQ)² = (PN)² + (NQ)²
∵ PQ = 39 ⇒ given
∵ PN = 15 ⇒ given
- Substitute them in the equation above
∴ (39)² = (15)² + (NQ)²
∴ 1521 = 225 + (NQ)²
- Subtract 225 from both sides
∴ 1296 = (NQ)²
- Take √ for both sides
∴ 36 = NQ
In Δ PNR
∵ m∠PNR = 90° ⇒ proved
- PR is the hypotenuse
∴ (PR)² = (PN)² + (NR)²
∵ PR = 17 ⇒ given
∵ PN = 15 ⇒ given
- Substitute them in the equation above
∴ (17)² = (15)² + (NR)²
∴ 289 = 225 + (NR)²
- Subtract 225 from both sides
∴ 64 = (NR)²
- Take √ for both sides
∴ 8 = NR
∵ QR = NQ + NR
∴ QR = 36 + 8
∴ QR = 44 inches
The length of QR is 44 inches
Learn more:
You can learn more about the triangles in brainly.com/question/4354581
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