Question

the flower garden is in the shape of right triangle. the longest side of the triangle measures 13m . one of the shorter sides is 7m longer than the other. find the length of the shortest side . ( hint : use the Pythagorean theorem : a² + b² = c².)

Answer 1

Answer:

The length of the shortest side = 5m

Explanations:

The longest side of the triangle is the hypotenuse

Longest side = 13 m

One of the shorter sides is 7m longer than the other

Therefore, the two short sides are x and x+7

where x represents the shortest side

Using the Pythagora's theorem.

The square of the longest side equals the sum of the squares of the two short sides

`\begin{gathered} 13^2=x^2+(x+7)^2 \\ 169=x^2+x^2\text{ + 14x + 49} \\ 2x^2\text{ + 14x }-120\text{ = 0} \\ x^2\text{ + 7x - 60 = 0} \\ \text{Solving the quadratic equation above} \\ x\text{ = 5, -12} \\ \text{The sidelength cannot be negative} \end{gathered}`

The shortest side length = x = 5m