Mathematics

Find the area and the perimeter of a square whose diagonal is 10 cm long.

Pythagoras Theorem

ICSE

10 Likes

Answer

Let each side of square be a cm.

Find the area and the perimeter of a square whose diagonal is 10 cm long. Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Since, sides of square are perpendicular to each other,

In right angle △ABC,

By pythagoras theorem,

⇒ AC² = AB² + BC²

⇒ 10² = a² + a²

⇒ 100 = 2a²

⇒ a² = 50

⇒ a = $\sqrt{50} = 5\sqrt{2}$ cm.

Perimeter = 4a = $20\sqrt{2}$ cm.

Area = a² = 50 cm².

Hence, perimeter = $20\sqrt{2}$ cm and area = 50 cm².

Answered By

8 Likes

Related Questions

In △PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a - b) = (c + d)(c - d).
View Answer