Question

the altitude of a right triangle is 7 cm than its base . if hypotenuse is 13 cm , find the other two sides.??

Answer 1

hey... here's ur solution,
let,
base = x
altitude = x - 7
hypotenuse = 13

according to pythe. thrm,
(13)² = (x )² + ( x -7 )²

169 = x² + x² - 14 x +49

169 = x² + x² - 14 x + 49
169 - 49 = 2 x² -14 x
120 = 2x² - 14x
2 x² - 14x -120 =0
hence,

x² -7 x - 60 =0
after factorisation,
x² +5 x - 12 x -60 =0
hence x = 5
now,
ans. ( 5,12)

Answer 2

Solution:

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Given:

The altitude of the right triangle is 7 cm than its base , hypotenuse is 13 cm,,.

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To Find:

It's other two sides,.

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Let the length of the base be x,.

So,

By pythagoras theorem,.

We can say,

=> (x)² + (x + 7)² = (13)²

=> x² + x² + 14x + 49 = 169

=> 2x² + 14x + 49 - 169 = 0

=> 2x² + 14x - 120 = 0

=> 2(x² + 7x - 60) = 0

=> x² + 7x - 60 = 0,.

=> x - 5x + 12x - 60 = 0

=> x(x-5) + 12 (x - 5) = 0

=> (x + 12) (x - 5) = 0,.

We know that,

anything multiplied by  0 equals 0,.

So,

We can say,

x + 12 = 0,

so, x ≠ -12,. (as, base of a triangle (length) can't be negative),.

x - 5 = 0,

x = 5,. (Base = 5cm).,.

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Length of base + 7 = height,.

x + 7 = 12cm,.

∴ Height of the triangle = 12 cm,.
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                                  Hope it Helps !!