Question

In a right angled triangle, the hypotenuse is 2 cm longer than the base and 4

cm longer than the shortest side. Find the lengths of the three sides of the

triangle. ​

Answer 1

Answer:

• 10 cm
• 8 cm
• 6 cm

Step-by-step explanation:

Given

• In a right angled triangle, the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side.

To find

• Lengths of three sides of the triangle.

Solution

Let the length of the hypotenuse be x cm.

Then, base = x - 2 cm and shortest side = x - 4 cm

So, by Pythagoras theorem,

• (x - 2)² + (x - 4)² = x²
• (x² - 4x + 4) + (x² - 8x + 16) = x²
• (x² - 10x - 2x + 20) = 0
• x(x - 10) - 2(x - 10) = 0
• (x - 2) = 0 (x - 10) = 0
• x = 10

Hence,

• Hypotenuse = 10 cm

• Base = 10 - 2 = 8 cm

• Shortest side = 10 - 4 = 6 cm

Answer 2

Answer:

let the hypotenuse be x

base be x - 2

shortest side be x- 4

by using Pythagoras theorem,

the answer will be —

• x = 10 = H

• x - 2 = 8 = B

• x - 4 = 6 = P