Question

PQR is a right angled triangle, if PQ = 9 cm, QR = 12 cm, (a)find the
area of ∆PQR (b) the length of PR (c) length of altitude QS.​

Answer 1

Answer:

a)54

b)15

Step-by-step explanation:

A)1\2*9*12

=9*6

=54cm^2

B)PQ^2+QR^2=PR^2

9^2+12^2=PR^2

81+144=PR^2

225=PR^2

PR=15cm

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Answer 2

The area of triangle = 54 $cm^{2}$

The length of  PR = 15 cm

The value of QS = 7.2 cm

Step-by-step explanation:

Triangle PQR is right angle triangle with right angle at Q.

PQ = 9 cm

QR = 12 cm

(a) Area of the triangle A = 0.5× PQ × QR

⇒ A = 0.5 × 9 × 12

⇒ A = 54 $cm^{2}$

Therefore the area of triangle = 54 $cm^{2}$

(b). From pythagoras Theorm

$PR^{2} = PQ^{2} + QR^{2}$

$PR^{2} = 9^{2} + 12^{2} \\PR^{2} = 81 + 144\\PR^{2} = 225\\PR = 15$

Thus the length of  PR = 15 cm

(c). From Δ PQR

PQ × QR = QS × PR

Put the values of PQ , QR & PR In the above formula

9 × 12 = QS ×  15

$QS = \frac{108}{15}\\ QS = 7.2 cm$

Thus the value of QS = 7.2 cm