MATH SOLVE

2 months ago

Q:
# One side of a right triangle is 2 cm shorter than the hypotenuse and 7 cm longer than the third side. find the lengths of the sides of the triangle.

Accepted Solution

A:

The right angles triangle has three sides including the hypotenuse which is opposite to the right angle.

If the hypotenuse - H

Then one side is - H - 2

Third side is 7 cm shorter then H-2

Therefore it’s H -2-7 = H -9

According to Pythagoras theorem

Square of hypotenuse = sum of the squares of the other 2 sides

H² = (H-9)² + (H-2)²

H² = H² -18H + 81 + H² -4H + 4

0 =H² -22H +85

This is a quadratic equation

0 = H² - 17H -5H +85

0 = H (H - 17) -5(H-17)

(H-17) (H-5) =0

H -17=0 or H-5=0

H could be 17 cm or 5 cm

If H =5 cm then

Side 1 -H-2 = 3 cm

And side 2 - H-9 = -4 cm

Since lengths cannot be negative values

H isn’t 5 cm

Therefore H =17 cm

1 side is H-2 = 15 cm

2nd side H -9 = 8 cm

Three sides are 17 cm, 15 cm and 8 cm

If the hypotenuse - H

Then one side is - H - 2

Third side is 7 cm shorter then H-2

Therefore it’s H -2-7 = H -9

According to Pythagoras theorem

Square of hypotenuse = sum of the squares of the other 2 sides

H² = (H-9)² + (H-2)²

H² = H² -18H + 81 + H² -4H + 4

0 =H² -22H +85

This is a quadratic equation

0 = H² - 17H -5H +85

0 = H (H - 17) -5(H-17)

(H-17) (H-5) =0

H -17=0 or H-5=0

H could be 17 cm or 5 cm

If H =5 cm then

Side 1 -H-2 = 3 cm

And side 2 - H-9 = -4 cm

Since lengths cannot be negative values

H isn’t 5 cm

Therefore H =17 cm

1 side is H-2 = 15 cm

2nd side H -9 = 8 cm

Three sides are 17 cm, 15 cm and 8 cm