In the given figure, AB = 16 cm, BC = 12 cm and CA = 6 cm; find the length of CD.

By formula, By pythagoras theorem, ⇒ (Hypotenuse) 2 = (Perpendicular) 2 + Base 2 Let CD be x cm. In right angle triangle ACD, By pythagoras theorem, ⇒ AC 2 = AD 2 + CD 2 ⇒ 6 2 = AD 2 + x 2 ⇒ 36 = AD 2 + x 2 ⇒ AD 2 = 36 - x 2 ........(1) In right angle triangle ABD, By pythagoras theorem, ⇒ AB 2 = AD 2 + BD 2 ⇒ 16 2 = AD 2 + (BC + CD) 2 ⇒ 256 = 36 - x 2 + (12 + x) 2 [From equation (1)] ⇒ 256 = 36 - x 2 + 12 2 + x 2 + 2(12)x ⇒ 256 = 36 + 144 + 24x ⇒ 256 = 180 + 24x ⇒ 24x = 256 - 180 ⇒ 24x = 76 ⇒ x = cm. Hence, CD = cm.

In triangle ABC, angle A = 90°, CA = AB and D is a point on AB produced. Prove that :
DC² - BD² = 2AB.AD.

View Answer Bookmark Now

In triangle ABC, AB = AC and BD is perpendicular to AC. Prove that :
BD² - CD² = 2CD × AD

View Answer Bookmark Now

In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1 : 3.
Prove that : 2AC² = 2AB² + BC².

View Answer Bookmark Now

In a quadrilateral ABCD, ∠A + ∠D = 90°, prove that : AC² + BD² = AD² + BC².

View Answer Bookmark Now

Mathematics

In the given figure, AB = 16 cm, BC = 12 cm and CA = 6 cm; find the length of CD.

Pythagoras Theorem

Related Questions

In triangle ABC, angle A = 90°, CA = AB and D is a point on AB produced. Prove that :
DC² - BD² = 2AB.AD.

In triangle ABC, AB = AC and BD is perpendicular to AC. Prove that :
BD² - CD² = 2CD × AD

In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1 : 3.
Prove that : 2AC² = 2AB² + BC².

In a quadrilateral ABCD, ∠A + ∠D = 90°, prove that : AC² + BD² = AD² + BC².

Mathematics

In the given figure, AB = 16 cm, BC = 12 cm and CA = 6 cm; find the length of CD.

Pythagoras Theorem

Related Questions

In triangle ABC, angle A = 90°, CA = AB and D is a point on AB produced. Prove that :DC2 - BD2 = 2AB.AD.

In triangle ABC, AB = AC and BD is perpendicular to AC. Prove that :BD2 - CD2 = 2CD × AD

In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1 : 3.Prove that : 2AC2 = 2AB2 + BC2.

In a quadrilateral ABCD, ∠A + ∠D = 90°, prove that : AC2 + BD2 = AD2 + BC2.

In triangle ABC, angle A = 90°, CA = AB and D is a point on AB produced. Prove that :
DC² - BD² = 2AB.AD.

In triangle ABC, AB = AC and BD is perpendicular to AC. Prove that :
BD² - CD² = 2CD × AD

In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1 : 3.
Prove that : 2AC² = 2AB² + BC².

In a quadrilateral ABCD, ∠A + ∠D = 90°, prove that : AC² + BD² = AD² + BC².