Question

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

Answer 1

Let base be x cm , then altitude will be (x-7) cm.

Now ,

By using pythagoras theorem-

132 = x2 + (x-7)2

169 = x2 + x2 + 49 - 14x

2x2 - 14x - 120 = 0

x2 - 7x - 60 = 0

x2 - 12x + 5x - 60 = 0

x ( x - 12 ) + 5 ( x - 12 ) = 0

Hence x = 12

sO , Altitude is 5 cm

AND. ,

base = 12cm

Answer 2

Answer:

Step-by-step explanation:

Let the base =X

If the altitude is 7 less than the base

Therefore, (x-7) = altitude

Hypotenuse = 13

By Pythagoras theorem ---

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

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

2x^2-14x=169-49

2x^2-14x=120

2x^2-14x-120=0

X^2-7x-60=0

By factorize -----

X^2-12x+5x-60=0

X(x-12) +5(x-12) =0

X-12 =0

X=12

And

X+5=0

X=-5

Hence X= 12

Therefore , altitude = x-7= 12-7 =5

And base =X=12

Hope it's helpful