Question

Calculate the length of the hypotenuse of a right-angled triangle if one legth is $3$ inches longer than the other one and the area of the triangle is $35$ square inches.

• A. $10$
• B. $\frac{\sqrt{35}}{2}$
• C. $7\sqrt{10}$
• D. $\sqrt{149}$

Answer 1

The correct option is D $\sqrt{149}$

Let the sides containing the right angle be $x$ and $y$.

The given condition says that $y=x+3$

Also, the area of the triangle being $35$ square inches, we have $xy=70$

$\Rightarrow x(x+3)=70$

i.e. $x^2+3x-70=0$

i.e. $x^2+10x-7x-70=0$

i.e. $(x+10)(x-7)=0$

Since $x$ is a positive number, $x=7$ in and therefore $y=10$ inches

Thus the hypotenuse $=\sqrt{49+100}=\sqrt{149}$