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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.

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

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Let;the;base;be;x;cm\*then;altitude;will;be;x-7;cm\*By;pythagorus \*Rightarrow x^2+(x-7)^2=13^2\*Rightarrow x^2+x^2+49-14x=169\* Rightarrow 2x^2-14x-120=0\*Rightarrow x^2-7x-60=0\*Rightarrow x^2-12x+5x-60=0\*Rightarrow x(x-12)+5(x-12)=0\*Rightarrow (x+5)(x-12)=0 \*Rightarrow x=-5,;x=12\* herefore length;can;not;be;negative;so,; x=12;cm\*So,;base;is;12;cm;and;height;is;5;cm\*

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Deependra Verma

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