Question

Help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!

Answer 1

Answer: the length of the shoter leg is 2,5 feet

the length of the longer leg is 6.5 feet

Explanation:

Let the length of the shoter leg is x feet

Than the length of the longer leg is (x+4) feet

We use Pythagoras' theorem:

`\displaystyle\\x^2+(x+4)^2=7^2\\\\x^2+x^2+2(x)(4)+4^2=7(7)\\\\2x^2+8x+4(4)=49\\\\2x^2+8x+16-49=49-49\\\\2x^2+8x-33=0\\\\D=b^2-4ac\\\\Hence,\\\\D=8^2-4(2)(-33)\\\\D=8(8)+8(33)\\\\D=64+264\\\\D=328\\\\√(D)=√(328) \\\\x=(-bб√(D) )/(2(a)) \\\\x=(-8б√(328) )/(2(2)) \\\\x=-6.5277\\otin (x > 0)\\\\x=2.5277\ feet\\\\x+4=2.5277+4\\\\x+4=6.5277\ feet`

Answer 2

Shorter leg = 2.5 ft

Longer leg = 6.5 ft

Explanation:

Pythagorean theorem:

Let the shorter leg = x ft

Longer leg = (x + 4) ft

Hypotenuse = 7 ft

`\sf x^2 + (x +4)^2 = 7^2`

x² + x² + 2*x*4 + 4² = 49

x² + x²+ 8x + 16 = 49

2x² + 8x + 16 - 49 = 0

2x² + 8x - 33 = 0

This is a quadratic equation. We can use the below mentioned formula to find the value of x.

a = 2 ; b = 8 ; c = -33

b² - 4ac = 8² - 4 * 2 * (-33)

= 64 + 264

=328

`\sf x = (-b \± √(b^2-4ac))/(2a)`

`\sf x = (-8 \±√(328))/(2*2)\\\\\\x= (-8 \±18.11)/(4)\\\\\\x =(-8+18.11)/(4) ; \ x=(-8-18.11)/(4) > > \text{this is rejected because sides of } \\\\ \text{a triangle cannot be measured in negative value}`

`\sf x = (-8+18.11)/(4)`

`\sf x = (10.11)/(4)\\\\x =2.5275`

x+ 4 = 2.5275 + 4 = 6.5275

Shorter leg = 2.5 ft

Longer leg = 6.5 ft