Question

In a right angle triangle if the sum of the squares of the sides making a right angle is 289 then what is the lenth of the hypotenuies

Answer 1

✬ Hypotenuse = 17 ✬

Step-by-step explanation:

Given:

• Sum of squares of side making right angle is 289.

To Find:

• What is the length of hypotenuse ?

Solution: Let ABC be a right angled triangle at B in which

• AB = Perpendicular
• BC = Base
• AC = Hypotenuse
• ∠ABC = 90°

Pythagoras Theorem : It states that sum of the squares of two side containing the right angle is always equal to square of the third side i.e hypotenuse.

Applying Pythagoras Theorem in ∆ABC

★ H² = B² + P² ★

$\implies{\rm }$ AC² = AB² + BC²

$\implies{\rm }$ 289 = AB² + BC²

$\implies{\rm }$ 289 = AC²

$\implies{\rm }$ √289 = AC

$\implies{\rm }$ √17 $\times$ 17 = AC

$\implies{\rm }$ 17 = AC

Hence, the length of hypotenuse of triangle is 17 cm.

Answer 2

$\bf{\underline{Question:-}}$

• In a right angle triangle if the sum of the squares of the sides making a right angle is 289 then what is the length of the hypotenuse.

$\bf{\underline{Given:-}}$

• sum of the squares of the sides making a right angle is 289.

$\bf{\underline{To\:Find:-}}$

• Length of hypotenuse = ?

$\bf{\underline{USING: PYTHAGORAS:THEOREM}}$

$\bf{\orange{ AB^2 = AC^2 + BC^2}}$

• (Sum of the square of side I.e., AC + AB = 289)

$\bf → AB^2 = AC^2 + BC^2$

$\bf → AB^2 = 289$

$\bf → AB^ = \sqrt{289}$

$\bf → AB = \sqrt{17 × 17}$

$\bf → AB^ = 17$

$\bf{\underline{Hence:-}}$

• The length of hypotenuse = 17 cm