Question

Tick (√) the correct answer.
a. Area of a right-angled triangle is 48 m². If one of its legs is 12 m, its base is
i. 6 cm
ii. 6 m
iii. 8 cm
iv. 8 m​

Answer 1

(iv) 8 m

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Answer 2

A n s w e r

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G i v e n

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• Area of a right-angled triangle is 48 m²

• One of its legs is 12 m

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F i n d

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• Its Base

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S o l u t i o n

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$\underline{\bold{\texttt{Area of right angled triangle :}}}$

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➠ $\sf \dfrac { 1 } { 2 } \times Leg1 \times Leg2$

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Where ,

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➻ Leg1 = Height

➻ Leg2 = Base

Or ,

➻ Leg1 = Base

➻ Leg2 = Height

Depending on the given condition

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Here in this question we are given that one leg of this triangle is 12 m

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In this question we are asked to find base hence we will assume the given leg to be height

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Legs of a right angled triangle are the two sides other then the hypotenuse i.e Base and height of a right angled triangle are referred as legs

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⟮ Putting the values ⟯

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➜ $\sf 48 = \dfrac { 1 } { 2 } \times Base \times 12$

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➜ $\sf 48 = Base \times 6$

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➜ $\sf Base = \dfrac { 48 } { 6 }$

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➨ Base = 8 m

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• Hence the other leg or the base is 8 m

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∴ Option iv) is correct

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Additional information

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Properties of right angled triangle

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• One angle is always 90° or right angle

• The side opposite angle 90° is the hypotenuse

• The hypotenuse is always the longest side

• The sum of the other two interior angles is equal to 90°

• The other two sides adjacent to the right angle are called base and perpendicular

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Perimeter of triangle

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• a + b + c

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Where ,

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➻ a = Length of 1st side

➻ b = Length of 2nd side

➻ c = Length of 3rd side

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Area of triangle

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• $\sf \dfrac { 1 } { 2 } \times Base \times Height$

• $\sf \sqrt { s(s - a)(s - b)(s - c) }$

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Where ,

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➻ a = Length of 1st Side

➻ b = Length of 2nd Side

➻ c = Length of 3rd Side

➻ s = Semi perimeter i.e Half of the perimeter

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Can be found as :

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$\sf s = \dfrac { a + b + c } { 2 }$

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Other then the right angled triangle there are 2 more types of triangle based on angles

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• Acute angle triangle : When the angle between any 2 sides is less than 90° it is called an acute angle triangle.

• Right angle triangle: When the angle between a pair of sides is equal to 90° it is called a right-angle triangle.

• Obtuse angle triangle: When the angle between a pair of sides is greater than 90° it is called an obtuse angle triangle.