Given:-

• Hypotenuse = 13cm

To Find:-

• the other two sides of right-angled triangle.

step-by-step solution:-

Let x be the base of the triangle, then the altitude will be (x−7).

By Pythagoras theorem,

• → x² +(x−7)² = (13)²
• → 2x² −14x + 49 − 169=0
• → 2x² −14x−120 = 0
• → x² − 7x − 60 = 0
• → x² − 12x + 5x − 60 = 0
• → (x − 12)(x + 5) = 0
• → x = 12,x = −5

Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and,

the altitude of the triangle will be 12−7 = 5cm.

Step-by-step explanation:

base = x

altitude = x - 7

by Pythagoras theorem

Base² + height² = hypotenuse ²

divide the above equation by 2 we get

since x= -5 is neglected as it is negative.