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,
