the altitude of a right triangle is 7cm less than its base. if the hypotenus is 13 cm the other two sides of triangle are equal to:
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Answered by
2
Answer:
Let x be the base of the triangle, then the altitude will be (x−7).
By Pythagoras theorem,
- x^2 + (x-7)^2 = 13^2
- 2x^2 - 14x - 49 - 169 = 0
- 2x^2 - 14x - 120 = 0
- x^2 - 7x - 60 = 0
- x^2 - 12x + 5x - 60 = 0
- (x - 12) (x + 5) = 0
- x = 12, x = −5
Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.
HOPE IT'S HELPFUL FOR YOU
Answered by
4
Answer:
☆Answered by Rohith kumar. R. maths
friend:-
Proof;-
●Let the base BC of a right triangle x cm
●So altitude (AB)= (x-7)cm
●And hypotheses is AC= 13cm.
☆According to phythagorous theorem
●we get that ,
●AC^2=AB^2+BC^2
(13)^2=(x-7)^2+x^2
169=x^2+48-14x+x^2
2x^2-14x-120=0(÷ it by 2)
●we get ,
x^2-7x-60=0
x^2-12x+5x-60=0
x (x-12)+5 (x-12)
x+5=0, x-12=0
x=-5 x=+12.
▪side of triangle never be negative so
▪the required side of a triangle is
▪12-7=5cm and BC= 12cm .
☆Hope it helps u mate
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☆Thank you.
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