Question

The altitude of a right triangle is $7$ cm less than its base. If the hypotenuse is $13$ cm, then the other two sides are

• A. $4.5$ cm, $11.5$ cm
• B. $4$ cm, $11$ cm
• C. $3.5$ cm, $10.5$ cm
• D. $5$ cm, $12$ cm

Answer 1

The correct option is D $5$ cm, $12$ cm

Let $x$ represent the base of the triangle then, altitude of the triangle, is $x-7$
Then, we have
$x^2+(x-7{)}^2={13}^2$
[$\because$ it is a right angled triangle]
$\Rightarrow x^2+x^2-14x+49=169$
$\Rightarrow 2x^2-14x-120=0$
Using the quadratic formula, we get
$x=\frac{14\pm \sqrt{196+960}}{4}$
$\Rightarrow x=\frac{140\pm 34}{4}$
$x=5$ and $x=12$
Therefore, the other two sides of the triangle are of length $5$ cm and $12$ cm.