Answers:
For original triangle, perimeter is 60. The area is 120.
The dilated triangle, perimeter is 180. The area is 1080.
Step-by-step explanation:
24 times 3=72
10 times 3=30
26 times 3=78
72+30+78=180
Perimeter of diliated triangle
1/2btimesh=area
1/2 30 times 72=1080 square units
Perimeter of original triangle
24+10+26=60 units
1/2 10 times 24=120 square units
From the picture attached,
Measure of the base of the small right triangle = 10 units
Height of the triangle = 24 units
Measure of the Hypotenuse = 26 units
Since, Perimeter of the triangle = Sum of the measures of the sides of the triangle
Therefore, Perimeter = 10 + 24 + 26
= 60 units
Area of the triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(10)(24)[/tex]
= 120 units²
Given triangle is dilated by a scale factor of 3 to form the bigger triangle,
Scale factor = 3
Since, expression for the scale factor is given by,
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original}}[/tex]
Therefore, length of the base of the dilated (bigger) triangle will be,
[tex]3=\frac{\text{Measure of the base of the original}}{10}[/tex]
Measure of the base of the original = 30 units
Height of the dilated triangle will be,
[tex]3=\frac{\text{Height of the dilated triangle}}{24}[/tex]
Height = 24 × 3
= 72 cm
Hypotenuse of the dilated triangle will be,
[tex]3=\frac{\text{Hypotenuse of the dilated triangle}}{26}[/tex]
Hypotenuse = 78 cm
Now the perimeter of the dilated triangle = 30 + 72 + 78
= 180 cm
Area of the dilated triangle = [tex]\frac{1}{2}(30)(72)[/tex]
= 1080 cm²
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