In figure given below, triangle ABC is right angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are mid-points of the sides AB and AC respectively, calculate (i) the length of BC (ii) the area of △ADE.

(i) In right angle triangle ABC, By pythagoras theorem, ⇒ AC 2 = AB 2 + BC 2 ⇒ 15 2 = 9 2 + BC 2 ⇒ BC 2 = 225 - 81 ⇒ BC 2 = 144 ⇒ BC = = 12 cm. Hence, BC = 12 cm. (ii) Given, D and E are midpoints of AB and AC. ∴ By mid-point theorem, DE = = 6 cm. Area of △ADE = = 13.5 cm 2 Hence, area of △ADE = 13.5 cm 2 .

If in △ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

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In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that
(i) 9AQ² = 9AC² + 4BC²
(ii) 9BP² = 9BC² + 4AC²
(iii) 9(AQ² + BP²) = 13AB²

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In the figure given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.

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In the figure given below, ∠BAC = 90°, ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find
(i) AC
(ii) AB
(iii) area of the shaded region.

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Mathematics

In figure given below, triangle ABC is right angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are mid-points of the sides AB and AC respectively, calculate (i) the length of BC (ii) the area of △ADE.

Pythagoras Theorem

Related Questions

If in △ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that
(i) 9AQ² = 9AC² + 4BC²
(ii) 9BP² = 9BC² + 4AC²
(iii) 9(AQ² + BP²) = 13AB²

In the figure given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.

In the figure given below, ∠BAC = 90°, ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find
(i) AC
(ii) AB
(iii) area of the shaded region.

Mathematics

In figure given below, triangle ABC is right angled at B. Given that AB = 9 cm, AC = 15 cm and D, E are mid-points of the sides AB and AC respectively, calculate (i) the length of BC (ii) the area of △ADE.

Pythagoras Theorem

Related Questions

If in △ABC, AB > AC and AD ⊥ BC, prove that AB2 - AC2 = BD2 - CD2.

In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that(i) 9AQ2 = 9AC2 + 4BC2(ii) 9BP2 = 9BC2 + 4AC2(iii) 9(AQ2 + BP2) = 13AB2

In the figure given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.

In the figure given below, ∠BAC = 90°, ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find(i) AC(ii) AB(iii) area of the shaded region.

If in △ABC, AB > AC and AD ⊥ BC, prove that AB² - AC² = BD² - CD².

In a right angled triangle ABC, right angled at C, P and Q are the points on the sides CA and CB respectively which divide these sides in the ratio 2 : 1. Prove that
(i) 9AQ² = 9AC² + 4BC²
(ii) 9BP² = 9BC² + 4AC²
(iii) 9(AQ² + BP²) = 13AB²

In the figure given below, ∠BAC = 90°, ADC = 90°, AD = 6 cm, CD = 8 cm and BC = 26 cm. Find
(i) AC
(ii) AB
(iii) area of the shaded region.