Question

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

Answer 1

Let x be the base of the triangle.
Then height (which is 7 less than base) = x-7.

If the hypotenuse is 13cm, then the triangle is a right angle triangle, and we will apply Pythagoras Theorem here.

If a = base = x, b = height = x-7 and c = hypotenuse = 13, then

a^2 + b^2 = c^2. Substituting the values of a, b and c in the equation we get

x^2 + (x-7)^2 = 13^2

x^2+x^2-14x+49 = 169

2x^2-14x-120 = 0

x = (14±sqrt(14^2+4*2*120))/4

x = (14±sqrt(196+960))/4 = (14±sqrt(1156))/4 = (14±34)/4

Therefore x = 48/4 or -20/4 = 12 or -5

Since x cannot be negative, it is 12.

Thus if base = 12, then height = base - 7 = 12-7 = 5.

Therefore, base = 12cm and height = 5cm.

Answer 2

here is ur answer mate.......,.