In the adjoining figure, △ABC is right angled at A, BC = 7.5 cm and AB = 4.5 cm. If the area of quad. ABCD is 30 cm² and DL is the altitude of △DAC, calculate the length DL.
Mensuration
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Question

In the adjoining figure, △ABC is right angled at A, BC = 7.5 cm and AB = 4.5 cm. If the area of quad. ABCD is 30 cm2 and DL is the altitude of △DAC, calculate the length DL.

KnowledgeBoat · Accepted Answer

Given, △ABC is right-angled at A. BC = 7.5 cm (hypotenuse) AB = 4.5 cm Area of quadrilateral ABCD = 30 cm2 In △ABC, By using pythagoras theorem, ⇒ BC2 = AB2 + AC2 ⇒ (7.5)2 = (4.5)2 + AC2 ⇒ 56.25 = 20.25 + AC2 ⇒ AC2 = 56.25 - 20.25 ⇒ AC2 = 36 ⇒ AC = = 6 cm. From figure, Area of △DAC = Area of quad. ABCD − Area of △ABC = 30 - 13.5 = 16.5 cm2. Hence, DL = 5.5 cm.

Mathematics

In the adjoining figure, △ABC is right angled at A, BC = 7.5 cm and AB = 4.5 cm. If the area of quad. ABCD is 30 cm² and DL is the altitude of △DAC, calculate the length DL.

Mensuration

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