Question

determine the perimeter and the area of the following triangles: a) 2.1 m 5.5 m b) 60 cm

Explanation:

Part a)

Step1: Find the hypotenuse using Pythagorean theorem

For a right - triangle with legs \(a = 2.1\space m\) and \(b=5.5\space m\), by the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).

$$c=\sqrt{(2.1)^{2}+(5.5)^{2}}=\sqrt{4.41 + 30.25}=\sqrt{34.66}\approx5.89\space m$$

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is \(P=a + b + c\).

$$P=2.1+5.5 + 5.89=13.49\space m$$

Step3: Calculate the area

The area \(A\) of a right - triangle is \(A=\frac{1}{2}\times a\times b\).

$$A=\frac{1}{2}\times2.1\times5.5 = 5.775\space m^{2}$$

Part b)

Step1: Note the side lengths

Since it is an isosceles right - triangle (marked with equal sides), the legs \(a=b = 60\space cm\). Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).

$$c=\sqrt{60^{2}+60^{2}}=\sqrt{3600+3600}=\sqrt{7200}=60\sqrt{2}\approx84.85\space cm$$

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is \(P=a + b + c\).

$$P=60+60 + 84.85=204.85\space cm$$

Step3: Calculate the area

The area \(A\) of a right - triangle is \(A=\frac{1}{2}\times a\times b\).

$$A=\frac{1}{2}\times60\times60=1800\space cm^{2}$$

Answer:

a) Perimeter: \(13.49\space m\), Area: \(5.775\space m^{2}\)
b) Perimeter: \(204.85\space cm\), Area: \(1800\space cm^{2}\)