i. In ∆LMN, ∠M = 90°.
Hence, side LN is the hypotenuse.
According to Pythagoras’ theorem,
l(LN)2= l(LM)2 + l(MN)2
∴ x2= 72 + 242
.∴ x2= 49 + 576
∴ x2= 625
∴ x2= 252
∴ x = 25 units
ii. In ∆PQR, ∠Q = 90°.
Hence, side PR is the hypotenuse.
According to Pythagoras’ theorem,
l(PR)2= l(PQ)2+ l(QR)2
∴ 412 = 92 + x2
∴ 1681 = 81 + x2
∴ 1681 – 81 = x2
∴ 1600 = x2
∴ x2= 1600
∴ x2= 402
∴ x = 40 units
iii. In AEDF, ∠D = 90°.
Hence, side EF is the hypotenuse.
According to Pythagoras’ theorem,
l(EF)2= l(ED)2+ l(DF)2
∴ 172= x2+ 82
∴ 289 = x2+ 64
∴ 289 – 64 = x2
∴ 225 = x2
∴ x2 = 225
∴ x2= 152
∴ x = 15 units
