Question

The longer leg of a right triangle is 7 cm longer than the shorter leg. The hypotenuse is 9cm longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

Given:

a.) The longer leg of a right triangle is 7 cm longer than the shorter leg.

b.) The hypotenuse is 9cm longer than the shorter leg.

Let,

a = length of the longer leg

b = length of the shorter leg

c = length of the hypotenuse

We get,

Equation 1:

a = b + 7

c = b + 9

Since it's been mentioned that the figure is a right triangle, we will be using the Pythagorean Theorem in getting the measure of the sides.

`\text{ a}^2+b^2=c^2`
`\text{ (b + 7)}^2+b^2=(b+9)^2`
`\text{ b}^2+14b+49+b^2=b^2\text{ + 18b + 81}`
`\text{ 2b}^2+14b+49\text{ - }b^2\text{ - 18b - 81 = 0}`
`\text{ b}^2\text{ - 4b - 32 = 0}`

`\mleft(b^2+4b\mright)+\mleft(-8b-32\mright)\text{ = 0}`
`b\mleft(b+4\mright)-8\mleft(b+4\mright)\text{ = 0}`

`\mleft(b+4\mright)\mleft(b-8\mright)\text{ = 0}`

Therefore,

b = -4 (b + 4)

b = 8 (b - 8)

Since a length is never a negative value, we can therefore conclude that the measure of the shorter leg is 8 cm.

ANSWER:

Longer leg = shorter leg + 7 = 8 + 7 = 15 cm

Hypotenuse = shorter leg + 9 = 8 + 9 = 17 cm

Shorter leg = 8 cm