Question

Sico can for
a triangle
(1) This
8. State which of the following will form triplet et
a right-angled triangle. Also, identify the right
angle if any
In 9, 60, 61
6 7. 10.6
tiff) 1.5, 2, 25.​

Answer 1

Answer:

(i)

In the right angled triangle LMN, ∠M = 90∘. Hence, side LN is the hypotenuse.

According to Pythagoras' theorem,

l(LN)2 = l(LM)2 + l(MN)2

⇒(x)2 = (7)2 + (24)2

⇒x2 = 49 + 576

⇒x2 = 625

⇒x2 = (25)2

⇒x = 25

∴ the value of x is 25.

(ii)

In the right angled triangle PQR, ∠Q = 90∘. Hence, side PR is the hypotenuse.

According to Pythagoras' theorem,

l(PR)2 = l(QR)2 + l(PQ)2

⇒(41)2 = (x)2 + (9)2

⇒1681 = x2 + 81

⇒x2 = 1681 − 81

⇒x2 = 1600

⇒x2 = (40)2

⇒x = 40

∴ the value of x is 40.

(iii)

In the right angled triangle EDF, ∠D = 90∘. Hence, side EF is the hypotenuse.

According to Pythagoras' theorem,

l(EF)2 = l(ED)2 + l(DF)2

⇒(17)2 = (x)2 + (8)2

⇒289 = x2 + 64

⇒x2 = 289 − 64

⇒x2 = 225

⇒x2 = (15)2

⇒x = 15

∴ the value of x is 15.