Question

The hypotenuse of right triangle is 52 centimeters long. The difference between the other two sides is 28 centimeters.

Answer 1

Answer:

The length of the perpendicular   = 20 meters

The length of the base  = 48 meters

Step-by-step explanation:

The hypotenuse of the triangle  = 52 meters

Let the Length of the perpendicular is = k meters

So, the length of the base = ( k + 28) m

Now, by PYTHAGORAS THEOREM , in a right angled triangle:

$(BASE)^{2} + (PERPENDICULAR)^{2} = (HYPOTENUSE)^{2}$

⇒ Here, $(k)^{2} + (k +28) ^{2} = (52)^{2}$

Also, by Algebraic Identity:

$(a+b) ^{2} = a^{2} + b ^{2} + 2ab\\ \implies (k+28) ^{2} = k^{2} + (28) ^{2} + 2(28)(k)$

So, the equation becomes:

$(k)^{2} +k^{2} + (28) ^{2} + 2(28)(k) = (52)^{2}$

or, $2k^{2} + 784+ 56k = 2704\\\implies k^{2} + 28k - 960 = 0$

or,$k^{2} + 48k -20 k - 960 = 0$

Solving the equation:

⇒ (k+48)(k-20) = 0  , or (k+48) = 0 , or (k-20) = 0

or, either  k = -48 , or k = 20

As k is the length of the side, so k ≠  - 48, k  = 20

Hence, the length of the perpendicular  = k = 20 meters

and the length of the base  is k + 28 = 48 meters