18. If the base of of a right angle triangle is twice the height of the triangle and
the hypotenuse is 125 CM then the measure of the base is: *
Answers
Given data :
- The base of of a right angle triangle is twice the height of the triangle.
- Hypotenuse of the right angle triangle is 125 cm.
To find : Measure of the base of the right angle traingle.
Solution :
Now, according to given,
→ base = 2 * height .....( 1 )
→ hypotenuse = 125 cm .....( 2 )
Now, we use pythagorus theorem
→ (hypotenuse)² = (base)² + (height)²
{from eq. ( 1 ) & eq. ( 2 ) }
→ ( 125 )² = ( 2 * height )² + ( height )²
→ ( 125 )² = 4 * ( height )² + ( height )²
→ ( 125 )² = 5 * ( height )²
→ 15625 = 5 * ( height )² i.e.
→ ( height )² = 15625/5
→ ( height )² = 3125
→ height = √3125
→ height = 25√5 cm
Now, from eq. ( 1 )
→ base = 2 * height
→ base = 2 * 25√5
→ base = 50√5 cm
Answer : Hence, the measure of the base of the right angle triangle is 50√5 cm.
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