 Hello and welcome to this session. Let us understand the following problem today. Altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. First of all, let us understand the key idea. This theorem, hypotenuse square is equal to side square plus base square in a right triangle. Now, let us write the solution. Given to us, its altitude is 7 cm less than its base. And hypotenuse is equal to 13 cm. So, we have to find base and altitude. Let the base be x cm. Therefore, u is equal to x minus 7 cm. Now, by Pythagoras theorem, in a right triangle triangle is equal to altitude square plus base square. So, we get our equations as, r is equal to x minus 7 the whole square plus x is 169 is equal to x 49 minus 14x is equal to x minus 120 is equal to 0. implies x square minus 7x minus 60 is equal to 0. Now, splitting the middle term, we get x square minus 12x plus 5x minus 60 is equal to 0. Now, taking x common, we get x minus 12 plus 5 common x minus 12 is equal to 0 which implies x minus 12 into x plus 5 is equal to 0. This implies x is equal to 12 and x is equal to minus 5. 12 is equal to 12 cm equal to 5 cm, 12 cm. So, this is the problem by now.