Let the base of the triangle be b units. Then its height would be b + 7 units.

Now, the expression for the area of the right-angled triangle is

$Area =\frac{1}{2} \times base \times height$

Therefore,

$2340=\frac{1}{2} \times b \times(b+7)$

$4680=b^{2}+7 b$

$b^{2}+7 b-4680=0$

Applying the method of completing the square, we get

$b^{2}+7 b-4680=0$

$b^{2}+2 \times b \times \frac{7}{2}+\left(\frac{7}{2}\right)^{2}-\left(\frac{7}{2}\right)^{2}-4680=0$

$\left(b+\frac{7}{2}\right)^{2}=\frac{49}{4}+4680$

$\left(b+\frac{7}{2}\right)^{2}=\frac{18769}{4}$

$\left(b+\frac{7}{2}\right)^{2}=\left(\frac{137}{2}\right)^{2}$

$b+\frac{7}{2}=\pm \frac{137}{2}$

Therefore, either $b+\frac{7}{2}=\frac{137}{2}$ or $b+\frac{7}{2}=-\frac{137}{2}$

Thus, b = 65 or b = - 72

Since b is the base of the triangle, it cannot be negative. Therefore, base = 65 units

Thus, the height would be b + 7 = 72 units

The Pythagoras theorem states that in a right-angled triangle,

$(Hypotenuse) ^{2}=($ Base $)^{2}+($ Height $)^{2}$

Therefore,

$(Hypotenuse) ^{2}=(65)^{2}+(72)^{2}$

= 4225 + 5184

=9409

$=(97)^{2}$

Therefore, hypotenuse = 97 units.

Pythagorean Triplet & Pythagoras Theorem