Question

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

• A. $4,7$
• B. $5,12$
• C. $3,10$
• D. None of these

Answer 1

The correct option is B $5,12$

It is given that the length of the hypotenuse is $13$ cm.
We know that $5,12,13$ is a Pythagorean triplet.
Hence, base will be $12$ cm.
And corresponding height is $5$ cm $=(12-7)$ cm.
Alternatively,
Let the base be $x$.
Hence height will be $x-7$.
Applying Pythagorean theorem, we get
${13}^2=x^2+(x-7{)}^2$
$2x^2-14x+49=169$
$2x^2-14x-120=0$
$x^2-7x-60=0$
$(x-12)(x+5)=0$
Now length cannot be negative.
Hence, length of the base is $12$ cm.
Hence, altitude is $12-7$ $=5$ cm