• 0
Guru

# The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. Q.5

• 0

How i solve the question of quadratic equations of exercise 4.2 of question no.5 by easy method. It is very important of board exam. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Share

1. Let us say, the base of the right triangle beÂ xÂ cm.

Given, the altitude of right triangle = (xÂ â€“ 7) cm

From Pythagoras theorem, we know,

Base2Â + Altitude2Â = Hypotenuse2

âˆ´Â x2Â + (xÂ â€“ 7)2Â = 132

â‡’Â x2Â +Â x2Â + 49 â€“ 14xÂ = 169

â‡’ 2x2Â â€“ 14xÂ â€“ 120 = 0

â‡’Â x2Â â€“ 7xÂ â€“ 60 = 0

â‡’Â x2Â â€“ 12xÂ + 5xÂ â€“ 60 = 0

â‡’Â x(xÂ â€“ 12) + 5(xÂ â€“ 12) = 0

â‡’ (xÂ â€“ 12)(xÂ + 5) = 0

Thus, eitherÂ xÂ â€“ 12 = 0 orÂ xÂ + 5 = 0,

â‡’Â xÂ = 12 orÂ xÂ = â€“ 5

Since sides cannot be negative,Â xÂ can only be 12.

Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 â€“ 7) cm = 5 cm.

• 0