Question

question 33
solve.
a lot is in the shape of a right triangle. the shorter leg measures 90 meters. the hypotenuse is 30 meters longer than the length of the longer leg. how long is the longer leg?
a 150 meters
b 120 meters
c 90 meters
d 180 meters

Explanation:

Step1: Let the length of the longer leg be \(x\) meters

Let the length of the shorter leg \(a = 90\) meters. The hypotenuse \(c=x + 30\) meters.

Step2: Apply the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\)

Substitute \(a = 90\), \(b=x\), \(c=x + 30\) into the Pythagorean theorem:

$$90^{2}+x^{2}=(x + 30)^{2}$$

Expand \((x + 30)^{2}\) using the formula \((m+n)^{2}=m^{2}+2mn+n^{2}\), where \(m=x\) and \(n = 30\). So \((x + 30)^{2}=x^{2}+60x+900\)
The equation becomes:

$$8100+x^{2}=x^{2}+60x+900$$

Subtract \(x^{2}\) from both sides:

$$8100=60x+900$$

Subtract 900 from both sides:

$$60x=8100 - 900=7200$$

Divide both sides by 60:

$$x=\frac{7200}{60}=120$$

Answer:

B. 120 meters