If the sides of a triangle are in the ratio 1 : : 1, show that it is a right-angled triangle.

Question

KnowledgeBoat · Accepted Answer

Let ABC be the triangle. Given, Sides of a triangle are in the ratio 1 : : 1. Let AB = x, BC = and AC = x. Squaring both sides we get : AB² = x², BC² = 2x² and AC² = x². ⇒ AB² + AC² = x² + x² = 2x² = BC². Since, ⇒ BC² = AB² + AC². ∴ Triangle ABC satisfies pythagoras theorem. Hence, proved that ABC is a right-angled triangle.

Mathematics

If the sides of a triangle are in the ratio 1 : : 1, show that it is a right-angled triangle.

Pythagoras Theorem

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Mathematics

If the sides of a triangle are in the ratio 1 : : 1, show that it is a right-angled triangle.

Pythagoras Theorem

Related Questions

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AB = AC = x; BC = 10 cm and the area of the triangle is 60 cm². Find x.

In △ ABC, ∠C = 90° and AC = BC, then AB² is equal to :
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2BC² - AC²