11. In the figure below, PQR is a right-angled triangle, right angled at P. A perpendicular line PS is drawn from P to QR.PR=5 cm and PQ=12cm. 2 5 cm R D. 25:144 C. 13:60 B. 13:17 A. 5:12 What is RS:SQ? (Note: The figure is not to scale.)
Answers
RS : QS = 25 : 144 in ΔPQR right angled at P where PS ⊥ QR and PR = 5 cm , PQ = 12 cm.
Given :
- PQR is a right-angled triangle, right angled at P
- A perpendicular line PS is drawn from P to QR.
- PR = 5 cm
- PQ = 12 cm
To Find :
- RS : SQ
Step 1:
Pythagorean Theorem:
"Square on the hypotenuse of a right-angled triangle is equal to the
sum of the squares of the other two perpendicular sides"
QR² = PQ² + PR²
=> QR² = 12² + 5²
=> QR² = 13²
=> QR = 13 cm
Step 2:
Area of Triangle = (1/2) x base x height
Area of Δ PQR = (1/2) x PQ x PR
Area of Δ PQR = (1/2) x QR x PS
Step 3:
Equate area
(1/2) x PQ x PR = (1/2) x QR x PS
=> PQ x PR = QR x PS
=> 12 x 5 = 13 x PS
=> PS = 60/13 cm
Step 4:
Solve for RS in ΔPRS
RS² = PR² - PS²
=> RS² = 5² - (60/13)²
=> RS² = (5/13)² (13² - 12²)
=> RS² = (5/13)² (5²)
=> RS = (5/13)5
=> RS = 25/13
Step 5:
Solve for QS in ΔPQS
QS² = PQ² - PS²
=> QS² = 12² - (60/13)²
=> QS² = (12/13)² (13² - 5²)
=> QS² = (12/13)² (12²)
=> QS = (12/13)(12)
=> QS = 144/13
Step 6:
Find required ratio
RS : QS = 25 : 144
Learn More:
Which of the following triplets are Pythagorean?a. (7,8,9)b. (10,11 ...
brainly.in/question/44137020
Write a pythagorean triplet whose smallest number is 10 - Brainly.in
brainly.in/question/10971386
using the concept of Pythagoras theorem construct a segment of ...
brainly.in/question/8399081
draw a tangent segment of length √12 cm the circle with centre o ...
brainly.in/question/13741684