The hypotenuse of a right triangle drawn by Kavya is 13 cm. One leg is 7 cm longer than the other. If the shorter leg is x cm, set up the equation in standard form using the Pythagoras theorem and find x.

Question

Accepted Answer

5. Legs are x and x + 7, so x^2 + (x + 7)^2 = 13^2 = 169. This gives 2x^2 + 14x + 49 = 169, i.e. 2x^2 + 14x - 120 = 0, or x^2 + 7x - 60 = 0 = (x - 5)(x + 12). Positive root x = 5 cm.

The hypotenuse of a right triangle drawn by Kavya is 13 cm. One leg is 7 cm longer than the other.
If the shorter leg is $x$ cm, set up the equation in standard form using the Pythagoras theorem and find $x$ .

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More Class 10 Standard Form and Roots practice

The hypotenuse of a right triangle drawn by Kavya is 13 cm. One leg is 7 cm longer than the other.If the shorter leg is x cm, set up the equation in standard form using the Pythagoras theorem and find x.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Standard Form and Roots practice

The hypotenuse of a right triangle drawn by Kavya is 13 cm. One leg is 7 cm longer than the other.
If the shorter leg is $x$ cm, set up the equation in standard form using the Pythagoras theorem and find $x$ .