Triangle rst has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. what is the area of triangle rst? round to the nearest square inch.

Question

yenoanh · Answer

The area of triangle rst which have sides 22 inches and 13 inches with perimeter 50 inches is 95 square inches.

We are given that the two sides of the triangle rst are 22 inches and 13 inches respectively. Also perimeter of the triangle rst is 50 inches.

We have to find the area of triangle to the nearest square inches.

Let the third side of the triangle rst be x.

Hence,

22 + 13 + x = 50 inch

35 + x = 50 inch

x = 50 – 35
x = 15 inches

Hence, the third side of the triangle is 15 inches.

We will use the Heron’s formula here to find the area of the triangle.

Heron’s formula = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Here,

s = Semi- perimeter

a, b, and c are sides of the triangle.

Hence,

[tex]s=\frac{50}{2} \\\\s=25 inches[/tex]

a = 22 inches

b = 13 inches

c = 15 inches

Hence,

Area of the triangle rst = [tex]\sqrt{25(25-22)(25-13)(25-15)}\\\\ \sqrt{25(3)(12)(10)} =\sqrt{5*5*3*3*2*2*5*2}=5*3*2\sqrt{5*2}=30\sqrt{10}[/tex]

We know that,

[tex]\sqrt{10}[/tex] ≈ 3.162277
Hence,

[tex]\sqrt{10} * 30[/tex] ≈ 94.86831 ≈ 95 square inches.

To learn more about Area of triangle, here

https://brainly.com/question/20934807

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niczorrrr · Answer

The  area  of the  triangle  is 94.9 square inches    For given question,  We have been given  triangle  RST has sides measuring 22 inches and 13 inches and a  perimeter  of 50 inches.  Let x be the third side of ΔRST  ⇒ 22 + 13 + x = 50  ⇒ x = 50 - 35  ⇒ x = 15  Let s = sum of three sides of the  triangle  / 2  s = (22 + 13 + 15)/2  s = 25  Now using the formula for the  area of the triangle ,  A = √[s × (s-a) × (s-b) × (s-c)]  Let a = 22 inches, b = 13 inches, c = 15 inches  Substituting the values,  ⇒ A = √[25 × (25 - 22) × (25 - 13) × (25 - 15)]  ⇒ A = √(25 × 3 × 12 × 10)  ⇒ A = √9000  ⇒ A = 94.9 square inches    Therefore, the  area  of the  triangle  is 94.9 square inches        Learn more about the  area of the triangle  here:  https://brainly.com/question/19305981  #SPJ4

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