Question

side of a right angle triangle is 3 cm more than thrice the other side if the area of the triangle is 884 square cm then find the hypotenuse of the triangle​

Answer 1

Question:

A side of right angle triangle is 3 cm more than thrice the other side if area of triangle is 84 square cm then find the hypotenuse of the triangle​.

Answer:

The hypotenuse of the triangle is 25 cm

Explanation:

Let the side of the right triangle be x.

Let the other side of the right triangle by $3x+3$

Given that the area of the triangle is $84 \ cm^2$

Substituting these values in the area of the triangle, we have,

$Area = \frac{1}{2} bh$

    $84=\frac{1}{2} (x)(3x+3)$

   $168=3\left(x^{2}+x\right)$

     $56=x^{2}+x$

Making it as a quadratic equation, we get,

         $x^{2}+x-56=0$

Solving the equation, we get,

 $x^{2}+8 x-7 x-56=0$

$x(x+8)-7(x+8)=0$

        $(x-7)(x+8)=0$

                            $x=7,-8$

Since, the value of x cannot be negative.

Thus, $x=7$ is one side of the right triangle.

The other side of the triangle is $3 x+3=3(x+1)=3(7+1)=3 \times 8=24 \mathrm{cm}$

Now, we shall find the value of the hypotenuse using the Pythagorean theorem.

Thus, we have,

$H=\sqrt{7^2+24^2}$

   $=\sqrt{49+576}$

   $=\sqrt{625}$

$H=25$

Thus, the length of the hypotenuse is 25 cm

Learn more:

(1) A side of right angle triangle is 3 cm more than thrice the other side if area of triangle is 84 square CM then find the hypotenuse of the triangle​

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(2) a side of a right angle triangle is 3cm more than thrice the other side. if the area of triangle is 84sq.cm Find the hypotenuse​

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