Question

Q.35: Reshma wishes to fit three rods in the shape of a right triangle. The hypotenuse is to be 2cm longer
than The base and 4cm longer than the altitude. What should be the length of rods?
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Answer 1

Answer:

The lengths of the rods are 10 cm, 8cm, and 6cm.

Step-by-step explanation:

Let the hypotenuse = x

The base = x -2

The altitude = x - 4

By Pythagoras theorem: The sum of the squares of the base and the altitude equals the square of the hypotenuse

Thus,

(x - 2)^2 + (x - 4)^2 = x^2

x^2 - 4x + 4 + x^2 - 8x + 16 = x^2

2x^2 -12x + 20 = x^2

x^2 -12x + 20 = 0

This is a quadratic equation

Solve using the quadratic formula:

x = [12 +/-√144 - 4x1x20]/2

x = [12+/- √64]/2

x = [12+/-8]/2

Either x = (12-8)/2 = 2

or x = (12+8)/2 = 10

We take x = 10

So,

Hypotenuse = 10 cm

Base = 10 - 2 = 8cm

Altitude = 10 - 4 = 6cm

∴ The lengths of the rods are 10cm, 8cm, and 6cm