Question

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

Answer 1

Question:

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

Answer:

Base: 5 cm

Step-by-step explanation:

• Let the base of right angle triangle be X cm
• Its altitude be (x - 7)cm

By Pythagoras theorem,

$\tt {x}^{2} + (x - 7) {}^{2} = {13}^{2} \\ \tt \: {x}^{2} + {x}^{2} + 49 - 14x = 169\\ \tt \: {2x}^{2} - 14x - 120 = 0\\ \tt \: {x}^{2} - 7x - 60 = 0\\ \tt \: {x}^{2} -12x + 5x - 60 = 0\\ \tt \: x(x - 12) + 5(x - 12) = 0\\ \tt \: (x - 12)(x + 5)$

Either x-12 or x+5=0

x=12,x=-5

Since, sides are always positive so it can be 12.

Base= 12 -7=5 cm

$\huge \bold {{@QianNiu}}$

Answer 2

Answer is in attachment.