Question

question 1 of 5
select the correct answer.
what is the perimeter of rectangle mnop, rounded to the nearest tenth of a meter?
67.6 m
79.2 m
88.1 m
76.5 m

Explanation:

Step1: Find the length of \( NP \)

In right - triangle \( ONP \), \(\sin30^{\circ}=\frac{NP}{OP}\). Since \( OP = 28m \) and \(\sin30^{\circ}=\frac{1}{2}\), then \( NP=\sin30^{\circ}\times OP=\frac{1}{2}\times28 = 14m \).

Step2: Find the length of \( ON \)

In right - triangle \( ONP \), \(\cos30^{\circ}=\frac{ON}{OP}\). Since \( OP = 28m \) and \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\), then \( ON=\cos30^{\circ}\times OP\approx0.866\times28 = 24.248m \).

Step3: Find the perimeter of rectangle \( MNOP \)

The perimeter formula of a rectangle is \( P = 2(l + w) \), where \( l = ON\) and \( w = NP \). So \( P=2(ON + NP)=2(24.248+14)=2\times38.248 = 76.496m\approx76.5m \).

Answer:

76.5m