The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 3cm, find the other two sides
Answers
Step-by-step explanation:
Corrected Question:-
The altitude of a right triangle is 7cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Given :-
The altitude of a right triangle is 7 cm less than its base.
The hypotenuse is 13 cm.
To find :-
The other two sides.
Solution :-
Let the base of the right angled triangle be X cm
The altitude of the right angled triangle
= 7cm less than the base
= base - 7 cm
= (X-7) cm
Therefore, The Altitude of the triangle
= (X-7) cm
Given that
Hypotenuse of the right angled triangle
= 13 cm
We know that
Pythagoras Theorem :
" In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides ".
=> Hypotenuse² = Base² + Altitude²
=> 13² = X²+(X-7)²
=> 169 = X²+X²-2(X)(7)+7²
Since, (a-b)² = a²-2ab+b²
Where, a = X , b = 7
=> 169 = X²+X²-14X+49
=> 169 = 2X²-14X+49
=> 2X²-14X+49-169 = 0
=> 2X²-14X-120= 0
=> 2(X²-7X-60) = 0
=> X²-7X-60 = 0/2
=> X²-7X-60 = 0
=> X²+5X-12X-60 = 0
=> X(X+5)-12(X+5) = 0
=> (X+5)(X-12) = 0
=> X+5 = 0 (or) X-12 = 0
=> X = -5 (or) X = 12
We know that
X can't be negative.
Therefore, X = 12 cm
If X = 12 cm then base = 12 cm
If X = 12 cm then Altitude = 12-7 = 5 cm
Answer :-
The other two sides of the given right angled triangle are 12 cm and 5 cm
Check:-
Base = 12 cm
Altitude = 5 cm
Hypotenuse = 13 cm
12²+5² = 144+25 = 169 = 13²
(5,12,13) is a Pythagorean triplet.
Therefore, 5 cm, 12 cm and 13 cm forms a right angled triangle.
5 cm , 12 cm and 13 cm are the three sides of the given right angled triangle.
Verified the given relations in the given problem.
Used formulae:-
→ (a-b)² = a²-2ab+b²
Used Theorem:-
Pythagoras Theorem :
Pythagoras Theorem :" In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides ".
Given:
Altitude = Base - 7cm
Hypotenuse = 3cm
Let base be x
According to Pythagoras Theorem
A² + B² = Hypotenuse²
x² + (x-7)² = 3²
x² + x² - 14x + 49 = 9
2x² - 14x + 40 = 0
[dividing by 2]
x² - 7x + 20 = 0
The Question has some wrong values... The answer u get is not possible to be in a triangle!