The lengths of the adjacent sides of the right angle of a right-angled triangle are (x - 2) cm and cm. If the length of the hypotenuse is 3 cm, then the value of x is : 1. 1 2. 2 3. 3 4. 4

Question

KnowledgeBoat · Accepted Answer

In right triangle ABC, By pythagoras theorem we get, Hypotenuse2 = Base2 + Height2 ⇒ AC2 = BC2 + AB2 ⇒ 32 = (x - 2)2 + ⇒ 9 = x2 + 4 - 4x + 4 × 2 x2 ⇒ 9 = x2 + 4 - 4x + 8x2 ⇒ 9x2 - 4x + 4 - 9 = 0 ⇒ 9x2 - 4x - 5 = 0 ⇒ 9x2 - 9x + 5x - 5 = 0 ⇒ 9x(x - 1) + 5(x - 1) = 0 ⇒ (9x + 5) = 0 or (x - 1) = 0 ⇒ x = - or x = 1 Since, length cannot be negative. ⇒ x = 1 cm. Hence, option 1 is the correct option.

Mathematics

The lengths of the adjacent sides of the right angle of a right-angled triangle are (x - 2) cm and cm. If the length of the hypotenuse is 3 cm, then the value of x is : 1. 1 2. 2 3. 3 4. 4

Pythagoras Theorem

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Mathematics

The lengths of the adjacent sides of the right angle of a right-angled triangle are (x - 2) cm and cm. If the length of the hypotenuse is 3 cm, then the value of x is : 1. 1 2. 2 3. 3 4. 4

Pythagoras Theorem

Related Questions

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The lengths of the diagonals of a rhombus are 5 cm and 12 cm. The length of each side of the rhombus is:
13 cm
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The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is :
3 cm
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7 cm
9 cm