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For finding AB and BC with the help of information given in the following figure, complete the following activity :[Figure: Δ ABC with ∠B = 90º; the sides AB and BC carry identical tick marks showing AB = BC, and the hypotenuse AC = \(\sqrt{8}\).]Act…

Q.3 (A)(2) For finding AB and BC with the help of information given in the following figure, complete the following activity :

[Figure: Δ ABC with ∠B = 90º; the sides AB and BC carry identical tick marks showing AB = BC, and the hypotenuse AC = \(\sqrt{8}\).]

Activity :

AB = BC .................... ____

∴ ∠BAC = ____

∴ AB = BC = ____ × AC

= \(\dfrac{1}{\sqrt{2}} \times\) ____

= \(\dfrac{1}{\sqrt{2}} \times 2 \times\) ____

AB = BC = ____

1 answer

Best answer

Answer: AB = BC = 2

AB = BC (given), so Δ ABC is an isosceles right-angled triangle with ∠B = 90º.

∴ ∠BAC = ∠BCA = 45º.

∴ AB = BC = \(\dfrac{1}{\sqrt{2}} \times AC = \dfrac{1}{\sqrt{2}} \times \sqrt{8} = \dfrac{1}{\sqrt{2}} \times 2 \times \sqrt{2}\) = 2.

Blanks in order: (given), 45º, \(\dfrac{1}{\sqrt{2}}\), \(\sqrt{8}\), \(\sqrt{2}\), 2.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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