Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides
Solution:
Given, the hypotenuse of a right triangle is 25 cm.
Out of the remaining two sides, one is longer than the other by 5 cm.
We have to find the lengths of the other two sides.
Let us consider a right triangle ABC with a right angle at B.
AC is the hypotenuse.
Let the length of the side AB = x cm
So, the length of the side BC = x + 5 cm
By using Pythagoras theorem for a right triangle,
AC² = AB² + BC²
So, (25)² = x² + (x + 5)²
By using algebraic identity,
(a +b)² = a² + 2ab + b²
So, (x + 5)² = x² + 10x + 25
Now, 625 = x² + x² + 10x + 25
625 = 2x² + 10x + 25
2x² + 10x + 25 - 625 = 0
2x² + 10x - 600 = 0
Dividing by 2,
x² + 5x - 300 = 0
On factoring,
x² + 20x - 15x - 300 = 0
x(x + 20) - 15(x + 20) = 0
(x - 15)(x + 20) = 0
Now, x + 20 = 0
x = -20
Also, x - 15 = 0
x = 15
Since a negative value is not possible, x = -20 is neglected.
So, the length of the side AB is x = 15cm
Now, BC = x + 5 = 15 + 5 = 20 cm
Therefore, the lengths of the other two sides are 20 cm and 15 cm.
✦ Try This: Hypotenuse of a right triangle is 16 cm and out of the remaining two sides, one is longer than the other by 2 cm. Find the lengths of the other two sides
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Sample Problem 2
Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides
Summary:
Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. The lengths of the other two sides are 15 cm and 20 cm
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