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The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Given:
The height of a right triangle is $7\ cm$ less than its base. The hypotenuse is $13\ cm$.
To do:
We have to find the other two sides.
Solution:
Let the length of the base be $x\ cm$.
The height of the triangle $=x-7\ cm$
Using the Pythagoras theorem,
$(x)^2+(x-7)^2=(13)^2$
$x^2+x^2+49-14x=169$
$2x^2-14x+49-169=0$
$2x^2-14x-120=0$
$x^2-7x-60=0$
$x^2-12x+5x-60=0$
$x(x-12)+5(x-12)=0$
$(x-12)(x+5)=0$
$x=12$ or $x=-5$
Length cannot be negative. Therefore,
$x=12\ cm$
$x-7=12-7=5\ cm$
The length of the base is $12\ cm$ and the height of the triangle is $5\ cm$.
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