Question

In the figures below, find the value of 'x'.

Answer 1

(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.