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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Answer:
can you send a pic of the graph so we can give you an answer?
You can graph it, the slope will be 1/2 and the y-int will be -3
A. r=1 d=2
hope this help
Explanation:
From the diagram, one square box represensts 1 units. The pre image of parallelogram ABCD is A'B'C'D' as shown. We can see that the parallelogram ABCD at the right shifted towards the left by 3 units (note the 1 unit represents one squaren
Hence we can conclude that the parallelogram ABCD shifts 3 units to the left to produce a pre-image A'B'C'D'ote the 1 unit represents one square)
Hence we can conclude that the para