Question

a) A side of a right angled triangle is 3 cm more than thrice the
other side. If the area of the triangle is 84 sq.cm, then find
the hypotenuse of the triangle.

Answer 1

Answer is given.

Take the base of triangle as x and other side as 3x+3.

The area is given and by the equation 1/2×base×height u can find x.

So that we got the side and by pythagoras theorem u will get the hypotenuse.

if u have any doubt ask me in the comment section

Answer 2

The hypotenuse of the right angled triangle(h) = 25 cm

Step-by-step explanation:

Let the one side of a right angled triangle(b) = x and

The other side of a right angled triangle (h) = (3x + 3)

Given, the area of the triangle = 84 $cm^{2}$

To find, the hypotenuse of the triangle (h) = ?

We know that,

The area of a right angled triangle = $\dfrac{1}{2} bh$

⇒ $\dfrac{1}{2} x(3x+3) = 84$

⇒ x(3x+3) = 84 × 2 = 168

⇒ $3x^{2} +3x-168=0$

Dividing by 3, we get

⇒ $x^{2} +x-56=0$

⇒ $x^{2} +8x-7x-56=0$

⇒ x(x + 8) - 7(x + 8) = 0

⇒ (x + 8)(x - 7) = 0

⇒ x + 8 = 0 or, x - 7 = 0

⇒ x = - 8 or, x = 7 [ ∵ -7 is not possibe because side never be negative]

⇒ x = 7

∴ 3x + 3 = 3 × 7 + 3 = 24

In a right angled triangle ,

Hypoyaneous, h = $\sqrt{b^{2}+ p^{2}}$

$=\sqrt{7^{2}+ 24^{2}}=\sqrt{49+576} =\sqrt{625} =25 cm$

Thus, the hypotenuse of the right angled triangle(h) = 25 cm