The shorter leg of a right triangle is 7ft shorter than the longer leg. the hypotenuse is 7ft longer than the longer leg. find the side lengths of the triangle

The answers are:

Since we are working with a right triangle, we can use the Pythagorean Theorem, which states that:

Then, we are given the following information:

Let be "a" the shorter leg and "b" the the longer leg of the right triangle, so:

We can see that we need to perform the notable product, so:

We have that the obtained equation will be equal to 0 if: b is equal to 0 or b is equal to 28:

So, since we are looking for the side of a leg, the result that we need its 28 feet.

Hence, we have that the answers are:

Have a nice day!

Base = 21 ft

Height = 28 ft

Hypotenuse =  35 ft

Step-by-step explanation:

It is given that,the shorter leg of a right triangle is 7ft shorter than the longer leg. The hypotenuse is 7ft longer than the longer leg

Let longer leg = x then shorter leg  = x - 7 and hypotenuse = x+ 7

To find the side lengths of triangle

Here Base = x-7

Height = x

Hypotenuse = x + 7

By using Pythagorean theorem we can write,

Base² + height² = Hypotenuse²

(x - 7)² + x² = (x + 7)²

x² -14x + 49 + x² = x² +14x + 49

x² - 14x = 14x

x² - 28x = 0

x(x - 28) = 0

x = 0 or x = 28

Therefore the value of x = 28

Base = x - 7 = 21

Height = 28

Hypotenuse = 28 + 7 = 35

d≈7.07in

step-by-step explanation: