Answer:
Hypotenuse = 87.2
Step-by-step explanation:
First find the lengths of the legs given the value of x
Left leg : 5x + 5
x = 13
5(13)+5
65 + 5 = 70
Bottom Leg : 4x
x = 13
4(13) = 52
So we have legs with lengths of 70 and 52 and knowing this we want to find the length of the hypotenuse.
We can do this by using the Pythagorean Theorem : a² + b² = c²
Where a and b = legs and c = hypotenuse
We are given the legs and we want to find the hypotenuse (c)
We can do this by plugging in the values of the legs into the Pythagorean Theorem and solving for c
Pythagorean Theorem : a² + b² = c²
a = 52 and b = 70
52² + 70² = c²
52² = 2704 and 70² = 4900
2704 + 4900 = c²
7604 = c²
take the square root of both sides
√7604 = 87.2 ( rounded to the nearest tenth ) and √c² = c
We're left with c = 87.2
The length of the hypotenuse is 87.2
